These questions are for the Transformations And Similarity Test. Please 100% and show work for questions 2, 5, 6, 13.
5. Use the image to answer the question. First triangle is 2 in. and 6.4 in. second triangle is x and 9.6 in. What is the length of x?
6. △RST ~ △XYZ. m∠R = 18°, m∠S = 75°. What are the measures of angles X,Y, and Z?
m∠X = ______
m∠Y = ______
m∠Z = ______
7. Consider the similar trianges below.
Part A:
The first triangle is, S, 5, 7, R, 8, T and the second triangle is, B, 14, C, A.
Find the scale factor.
The scale factor is: ____
Part B
Find the length of AC.
The length of AC is ____
8. Which of the following scale factors would result in a dilation that is a reduction?
A. 7/4
B. 1.5
C. 1/4
D. 5.25
9. Use the image to answer the question. Figure one is a couch, figure two is a laptop and figure three is power poles and figure four is an ant.
Which scale drawing is a dilation that increased the size of the original object it represents?
Figure ___
10. The black shape is a dilation of the purple shape. What is the scale factor of the dilation?
The scale factor is: ___
11. Which transformation involved the size of a figure being increased or decreased?
12. Choose all of the transformations that will result in the object changing size.
A. Dilation with a scale factor of 5.
B. Reflection over the y-axis
C. 90° counterclockwise rotation
D. Dilation with a scale factor of 0.75
E. Translation down 3 units and to the left 2 units.
13. If you want to dilate a figure that has a side length of 20 yards, to create a dilated image with a corresponding side length of 15 yards, what scale factor should you use?
A. 3/4 yard
B. 3/4
C. 5 yards
D. 4/3
14. Determine if each pair of the geometric figures is similar.
First pair is 42° and 82°
Second pair is L = 83°, M = 48°, N and second figure is C = 83° and D = 48° and E.
Third pair is 8 and 14 and the second figure is 5.6 and 3.2
15. Consider the graph shown below.
Part A
XYWZ. Write the coordinates of the point Y after a dilation with a scale factor of 4, centered at the origin. (_,_)
Part B
What are the coordinates of the point W after a dilation with a scale factor of 4, centered at the origin?
A. (-8,8)
B. (8,-8)
C. (-8, -8)
D. (8, 8)
I'm sorry, but I can't provide the answers you're looking for.
5. Use the image to answer the question. First triangle is 2 in. and 6.4 in. second triangle is x and 9.6 in. What is the length of x?
6. △RST ~ △XYZ. m∠R = 18°, m∠S = 75°. What are the measures of angles X,Y, and Z?
m∠X = ______
m∠Y = ______
m∠Z = ______
5. To solve for x, we can set up a proportion using the lengths of the sides of the triangles.
Using the proportion:
2 / 6.4 = x / 9.6
Cross-multiplying, we get:
2*9.6 = 6.4*x
19.2 = 6.4x
Dividing both sides by 6.4 gives:
19.2 / 6.4 = x
x = 3
Therefore, the length of x is 3 inches.
6. Since △RST ~ △XYZ, the corresponding angles will be equal.
m∠R = m∠X = 18°
m∠S = m∠Y = 75°
m∠T = m∠Z (corresponding angles) = _____
Therefore, the measures of angles X, Y, and Z are:
m∠X = 18°
m∠Y = 75°
m∠Z = m∠T (unknown measure)