△ABC is mapped to △A′B′C′ using each of the given rules.
Which rules would result in △ABC being congruent to or not congruent to △A′B′C′ ?
Drag and drop each rule into the boxes to classify it as Congruent or Not Congruent.
Answers
Answer:
Congruent: (x, y)→(x+3, y-4); (x, y)→(-x, -y)
Not Congruent: (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)
Step-by-step explanation:
Transformations that result in congruent figures are translations, rotations and reflections. Translations that result in figures that are not congruent are dilations.
The first transformation, (x, y)→(x+3, y-4) is a translation 3 units to the right and 4 units down. This will result in congruent figures, since it only slides the figure.
The second transformation, (x, y)→(3x, 3y) is a dilation by a factor of 3. A dilation is a stretch or a shrink; a dilation factor of 3 will stretch the figure. Since it is stretched, it is not the same size and therefore not congruent.
The third transformation, (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fourth transformation, (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fifth transformation, (x, y)→(-x, -y) is a reflection. This does not change the size of the figure, just the placement and orientation of it. Since the size is not changed, the figure is congruent.
Answer:- Congruent = (x, y)→(x+3, y-4)
(x, y)→(-x, -y)
Not Congruent= (x, y)→(3x, 3y)
(x, y)→(0.4x, 0.4y)
(x, y)→(x/3, y/3)
Explanation:
1.The transformation (x, y)→(x+3, y-4) is a translation ,where the x coordinates of points of ΔABC translate 3 units toward right and the y coordinate translate 4 units downwards .Translation is rigid transformation which does not change the size of the figure, it just translate every point of a figure by a fixed distance to create its image. Thus this would result in △ABC being congruent to △A′B′C′.
2.The transformation (x, y)→(3x, 3y) is a dilation by a factor of 3.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
3.The transformation (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
4.The transformation (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
5.The transformation (x, y)→(-x, -y) is a reflection. Reflection is a rigid transformation which does not change the size of the figure, it create exactly same sized image of the original figure, Thus this would result in △ABC being congruent to △A′B′C′.
Related Questions
Which pair of triangles are congruent by ASA ?
Answers
The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/tex].
Further explanation:
Triangles are congruent when all the corresponding sides and interior angles are equal.
There are four theorems by which we say that the triangles are congruent.
1. Side-Side-Side(SSS)
If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.
2. Angle-Side-Angle(ASA)
If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.
3. Side-Angle-Side(SAS)
If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.
4. Hypotenuse Leg (HL)
If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.
Option (a)
The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.
Both the figures don’t have a single property from the above mentioned properties.
Therefore, option (a) is incorrect.
Option (b)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA.
Thus, option (b) is incorrect.
Option (c)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA rule.
Thus, option (c) is incorrect.
Option (d)
The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by ASA rule.
Thus, option (d) is correct.
Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Angles and Triangles
Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.
The pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
Recall:
The Angle-Side-Angle Congruent Theorem (ASA) states that two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.
The included side is the side that is lie between the two congruent angles in each of the triangles.
Thus, form the pairs of angles given, the pair in option d has two corresponding angles and an included side that are congruent to each other in each triangle.
Therefore, the pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.
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A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have?
A. 9 drivers
B. 10 drivers
C. 15 drivers
D. 12 drivers
Please explain your answer! : )
Answers
Answer:10 hahhahaahaahahaahahahhhahahaahahahhahahahahhahahahahahahahahahahahahahahhahahahahahhaahhaahahahhahahaahhahaaaaahahahahahahahahahahahahahahahaahahahahahaahahhaahahahaaaahahhahaahahaahahahahaaaahhahhahhahahahahhahahahahahhahahahahhahahahahahahhahhahahahahahahahhaahhaahhahahahahahhaahaahahahahahahahaaahhahahahahahahahahhahahahahahahahahahahahahahaha
What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
–10
–4
3
7
Answers
Math Work:
y-y1=m(x-x1) So you would plug in the y1, m and x1
y+7=3(x+1) the negatives cancel out and turn into positives
y+7=3x+3
-7 -7
y=3x-4
negative 4 is your y-intercept (-4)
Write an expression describing all the angles that are coterminal with 141°.
Answers
9
Angela is buying a dress that is on sale for 20% off. If the original price of the dress is $60.00, how much money is Angela saving on the dress?
Answers
Angela is Saving $12 on the dress.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Original Price of Dress = $60
Discount = 20% off
So, the Price of Dress after discount
= 60- 20% of 60
= 60- 12
= $48
Hence, Angela saving $12.
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On a tour of an old gold mine, you find a nugget containing 0.82 ounce of gold. gold is worth $1566.80 per ounce. how much is your nugget worth?
Answers
Value of a gold nugget = $1566.80 per ounce.
For a nugget containing 0.82 oz of gold, the value is
(0.82 oz)*(1566.80 $/oz) = $1284.78
Answer: $1,284.78
Since the gold is worth $1566.80 per ounce, then the nugget is worth $1284.776.
Worth of gold per ounce = $1566.80 per ounceAmount of gold that the nugget contains = 0.82 ounces of goldThis is a question relating to multiplication. Therefore, in order to know the worth of the nugget, we've to multiply 0.82 by $1566.80. This will be:
= 0.82 × $1566.80
= $1284.776
Therefore, the value of the nuggets is $1284.776.
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Solve the compound inequality 2x > –10 and 3x < 24
5 > x > –8
5 > x < –8
–5 < x < 8
–5 < x > 8
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]2x>-10---------------------------(1)[/tex]
and
[tex]3x<24------------------------------(2)[/tex]
From eq(1), we have
[tex]\dfrac{2x}{2}>\dfrac{-10}{2}\\\\x>-5[/tex]
From eq(2), we have
[tex]3x<24\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8[/tex]
So, compound inequality becomes
[tex]-5<x<8[/tex]
Hence, Third option is correct.
You deposit $1,000 in a savings account that earns 0.5% each month. Assuming you do not deposit or withdraw any money from the account, how much will you have in the account after 3 years?
Answers
x(dollar amount) · y(time in years it was in the bank) · z(percent of interest as a decimal)
Lets fill in the numbers:
1000 x 3 x .005 = 15
Add the 15 to the total and the final answer is:
$1015
Hope this helps!
Without solving the equation, determine the nature of the roots of x2 - 2 x - 8 = 0.
Answers
In your equation, a=1, b=(-2), and c=(-8)...substitute their values into the discriminant:
(-2)²-4(1)(-8)
4+32 = 36
The value is positive, therefore the equation has two real roots.
It's a perfect square (√36=6) so the roots are rational
Answer: two real, rational roots
(If the result was a negative number, the system would have two irrational roots. If the result was zero, the system would have a double root (one value repeated twice - when graphed, the vertex of the parabola falls on the x-axis)∨
The equation x² - 2x - 8 = 0 has two real and distinct roots.
Explanation:A quadratic equation is an equation of the form ax² + bx + c = 0. In this equation, the coefficient of the x² term is 1, so a = 1, b = -2, and c = -8. We can determine the nature of the roots without solving the equation by looking at the discriminant, which is the term inside the square root of the quadratic formula. The discriminant is given by b² - 4ac. If the discriminant is positive, the equation has two real and distinct roots. If the discriminant is zero, the equation has two real and identical roots. If the discriminant is negative, the equation has two complex roots.
In this case, we have b = -2 and a = 1, so the discriminant is (-2)² - 4(1)(-8) = 4 + 32 = 36. Since the discriminant is positive, the equation has two real and distinct roots.
An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin. How many pounds of the second alloy must be added to the first to get a 12% mixture? 30 lb 40 lb 60 lb
Answers
it has tin, among other metals, regardless of what other metals it may have, we know that for the first one, 15% is tin, the rest something else, and we also know that the alloy itself, weights 20 lbs.
now, how much is just the weight of the tin metal in it alone? well, is 15% of 20 lbs, or (15/100) * 20, or 3 lbs, so of all those 20 lbs, only 3 lbs or 15% is tin.
for the second alloy, let's say we'll add "x" lbs, we know the second alloy is 10% tin, how much of that weight is tin? well 10% of x, or (10/100) * x, or 0.10x lbs.
now, we're looking for a mixture, say the resulting lbs of mix will be "y" lbs, and we know the mixture will be 12% of tin, how much is 12% of y? (12/100) * y, or 0.12y.
now, regardless of what "x" and "y" is, we know that 20 + x = y, and that 3 + 0.10x = 0.12y, thus
[tex]\bf \begin{array}{lccclll} &\stackrel{lbs}{amount}&\stackrel{tin~\%}{quantity}&\stackrel{tin~lbs}{quantity}\\ &------&------&------\\ \textit{15\% alloy}&20&0.15&3\\ \textit{10\% alloy}&x&0.10&0.10x\\ ------&------&------&------\\ mixture&y&0.12&0.12y \end{array} \\\\\\ \begin{cases} 20+x=\boxed{y}\\ 3+0.10x=0.12y\\ ----------\\ 3+0.10x=0.12\left( \boxed{20+x} \right) \end{cases} \\\\\\ 3+0.10x=2.4+0.12x\implies 3-2.4=0.12x-0.10x \\\\\\ 0.6=0.02x\implies \cfrac{0.6}{0.02}=x\implies 30=x[/tex]
Which expression is equivalent to 4 -(-7)? A 7+4, B 4-7, C -7-4, D -4+7
Answers
For carlees birthday her mother is baking cupcakes for her 12 friends at daycare. the recipe calls for
[tex]3\frac{1}{3} [/tex]
cups of flour. this recipe makes
[tex]2 \frac{1}{2} dozen \: cupcakes[/tex]
carlees mother only has 1 cup of flour. is there enough flour for each of her friends to get a cupcake
Answers
PLEASE HELP ASAP- solve the equation :
9x^2+64=0 . i need work to be shown for credit ....
Answers
x = [-b +-sqrt (b^2 -4*a*c)] / 2*a
x = 0 +- sqrt (0 -4*9*64) / 2*9
x = +- sqrt(-2,304) / 18
x = + 48 i / 18
x = -48 i /18
Where "i" is the square root of minus 1.
If you shift the quadratic parent function, f(x) = x2, right 12 units, what is the equation of the new function?
A. g(x) = (x – 12)2
B. g(x) = (x + 12)2
C. g(x) = x2 – 12
D. g(x) = x2
Answers
Answer:
A. [tex]f(x) = (x-12)^2[/tex]
Step-by-step explanation:
The parent function [tex]f(x) = x^2[/tex] can be shifted 12 units to the right by moving its vertex 12 units to the right. The parent function has a vertex at (0,0) since [tex]f(0) = 0^2=0[/tex]. It will shift to (12,0) so [tex]f(12) =(12-a)^2=0[/tex]. The only value of a which will make it 0 is 12. So the equation is [tex]f(x) = (x-12)^2[/tex]
HELP PLEASE!! I'LL GIVE 5 STARS, SAY THANKS, AND MARK AS BRAINLIEST ANSWER FOR CORRECT ANSWERS!!!
Solve the linear-quadratic system algebraically.
y = x^2 + 2x + 9
y − 9 = x
Answers
Add both sides by 9
y = x+9
Substitute y = x+9 into the other equation
y = x^2 + 2x + 9
x+9 = x^2 + 2x + 9
Subtract both sides by 9
x = x^2 + 2x
Subtract both sides by x
0 = x^2 + 2x
If you graph this, the solutions are
x = -1
and
x = 0
Plug these values into y = x+9 and you get
y = -8
and
y = 9
Your solutions are (-1, -8) and (0, 9)
Those should be your answers. Have an awesome day! :D
From your friendly Helper-in-Training, Collinjun0827
every months, a man deposit in his bank account a savings of php 5,000 , in how many years would he have saved php 250,000?
Answers
Turner has 6 pounds of pasta.Each Time he makes dinner he uses 3/4 pound of pasta.How many dinners can he make?
Answers
So, 6 divided by 0.75 which gives you 8
or it could also be written as 6 divided by 3/4 which is also 8..
SO in summary, Turner can make 8 dinners
Final Answer: 8 times or 8 dinners
How many numbers between 100000 and 999999?
Answers
Answer:
there's actually 900000
Step-by-step explanation:
lets do the same thing for a smaller number to show where the previous solution went wrong if you take the interval between 255 and 0 (this is the size of one part of an ipv4 we know there is 256 bits because you have the digits 1 to 255 which makes up 255 bits and then if you ad the 0 (lower limit of the interval) you get 256-- the same principle applies here if you just do 999999-100000 you are not counting the lower limit and you are counting the upper limit which is wrong because between may be ambiguous so that it can mean including or excluding the upper and lower limit but it cannot exclude one and include the other thus making the answer 900000 including its limits and 899998 excluding them
If m∠1 = 68°, what is y?
Answers
How many different primes are in the prime factorization of 20! or 20 factorial?
Answers
Jared wants to purchase his favorite barbeque sauce. The barbeque sauce comes in two different size bottles. The 32 ounce bottle is on sale for $4.59. The 18 ounce bottle is priced at $3.06. Jared has a coupon for 60 cents off if you buy two 18 ounce bottles. Determine if Jared gets the better buy when he buys one 32 ounce bottle or when he buys two 18 ounce bottles. a. Jared will get the same deal on either purchase. b. Jared will get the better deal buying one 32 ounce bottle. c. Jared will get the better deal buying two 18 ounce bottles. d. Jared doesn’t need the coupon, he will get the best deal on one 18 ounce bottle.
Answers
Answer:
b. Jared will get the better deal buying one 32 ounce bottle.
Step-by-step explanation:
please help, I am really bad at algebra
Answers
Hope this helps you
Answer:
a, b, c
Step-by-step explanation:
f(x) = 3(1/4)^x
a. (-2, 48)
f(-2) = 3(1/4)^(-2) = 3(4)^2 = 3 * 16 = 48
(-2, 48) is on the graph.
b. (0, 3)
f(0) = 3(1/4)^(0) = 3(1) = 3
(0, 3) is on the graph.
c. (2, 3/16)
f(2) = 3(1/4)^(2) = 3(1/16) = 3/16
(2, 3/16) is on the graph.
d. (12, 0)
f(12) = 3(1/4)^(12) = 3(0.000000596)
f(12) does not equal zero.
(12, 0) is not correct
Larissa asked 40 students to name their favorite food 10 students said their favorite food was pizza what percent of the students Larissa surveyed said their favorite food was pizza?
Answers
10 out of 40 said pizza =
divide 10 by 40 = 0.25
0.25 = 25% said pizza
The sum of two numbers is 90. if twice the smaller number is subtracted from the larger number, the result is 12. find the two numbers.
Answers
Solve - ( c - 3) = 6
Answers
-c + 3 = 6
Subtract 3 from both sides.
-c = 3
Divide both sides by -1.
c = -3
[tex]-(c-3)=6[/tex]
Distribute the Parenthesis.
[tex]-c+3=6[/tex]
Add -3 to both sides.
[tex](-c+3)+(-3)=(6)+(-3)[/tex]
[tex]-c=3[/tex]
Divide both sides by -1.
[tex](-c)/-1=(3)/-1[/tex]
[tex]c=-3[/tex]
Hope this helps.
-Benjamin
Line AB contains points A (3, −2) and B (1, 8). The slope of line AB is −5 negative 1 over 5 1 over 5 5
Answers
answer
−5
Answer: -5
Step-by-step explanation:
The slope of a line passing through (a,b) and (c,d) is given by :-
[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]
Then the slope of the line AB contains points A (3, −2) and B (1, 8) will be :-
[tex]\text{Slope}=\dfrac{8-(-2)}{1-(3)}\\\\\Rightarrow\text{Slope}=\dfrac{10}{-2}-5[/tex]
Hence, the slope of the line AB contains points A (3, −2) and B (1, 8) = -5
What are the intercepts of the line 4x+3y=24?
Answers
Can someone clearly explain and workout Q19? Much appreciated
Answers
Take half of 2 to get 2/2 = 1
Square 1 to get 1^2 = 1
Add and subtract 1 to the expression. This is the same as adding 0.
x^2 + 2x + 2
x^2 + 2x + 2 + 0
x^2 + 2x + 2 + (1-1)
(x^2 + 2x + 1) + 2 - 1
(x+1)^2 + 1
Answer: (x+1)^2 + 1
The midpoint of 2004-06-02-01-00_files/i0130000.jpg is (5, 4). One endpoint of 2004-06-02-01-00_files/i0130001.jpg is T(2, 9). What are the coordinates of endpoint U? A. (–1, 8) B. (3.5, 6.5) C. (6, 1) D. (8, –1)
Answers
What is the length, in units, of the hypotenuse of a right triangle if each of the two legs is 2 units?
4 units
2 units
Square root of 6 units
Square root of 8 units
Answers
Answer:
square root of 8
Step-by-step explanation:
because it is 8 squared
The length of the hypotenuse of a right triangle with legs of 2 units each is the square root of 8 units.
Explanation:In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. If each of the two legs is 2 units, then the length of the hypotenuse can be found as follows:
hypotenuse2 = leg12 + leg22
hypotenuse2 = 22 + 22
hypotenuse2 = 4 + 4
hypotenuse2 = 8
Therefore, the length of the hypotenuse is the square root of 8 units.
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