Grade 8 Math Practice Test: Dilations and Similar Triangles
- Dilations and Similar Triangles
- 10 questions
- 15 minutes
This test covers dilations centered at the origin, scale factors, similar figures and the angle-angle (AA) test for similar triangles. Tip: a scale factor greater than 1 enlarges a figure, and a scale factor between 0 and 1 shrinks it.
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Question 1
Point P(6, −4) is dilated by a scale factor of 12 with the center of dilation at the origin. What are the coordinates of its image?
Correct answer: A
Multiply each coordinate by 1/2: (6 · 1/2, −4 · 1/2) = (3, −2). (12, −8) multiplies by 2 instead, and (5.5, −4.5) subtracts 1/2.
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Question 2
A rectangle that is 4 cm by 6 cm is dilated by a scale factor of 2.5. What is the perimeter of the image?
Correct answer: B
The image is 10 cm by 15 cm, so its perimeter is 2(10 + 15) = 50 cm. Equivalently, 2.5 × 20 cm. 30 cm adds 2.5 to each side instead of multiplying.
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Question 3
A triangle with sides 15, 20 and 25 units is dilated. The image has sides 6, 8 and 10 units. What is the scale factor?
Correct answer: C
Scale factor = image length ÷ original length = 6 ÷ 15 = 2/5 (and 8/20 and 10/25 give the same). 5/2 divides the original by the image, and 9 is a difference, not a ratio.
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Question 4
A figure is dilated by a scale factor of 34. Which statement about the image is true?
Correct answer: C
A scale factor between 0 and 1 shrinks the figure, and every length is multiplied by 3/4. Angle measures stay the same.
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Question 5
Triangle ABC has angles of 40° and 75°. Triangle DEF has angles of 75° and 65°. Are the triangles similar?
Correct answer: A
The third angle of ABC is 180 − 40 − 75 = 65°, so both triangles have angles 40°, 65° and 75°. Two equal pairs of angles are enough (AA similarity). One shared angle alone is not enough.
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Question 6
A 6-foot-tall person casts a 4-foot shadow. At the same time, a tree casts an 18-foot shadow. How tall is the tree?
Correct answer: B
The sun's rays make similar triangles, so height ÷ shadow is the same: 6/4 = h/18, and h = 18 × 1.5 = 27 feet. 20 feet adds the 2-foot difference instead of using a ratio.
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Question 7
Triangle ABC is similar to triangle DEF, with A matching D, B matching E and C matching F. AB = 8 cm, BC = 12 cm and DE = 10 cm. What is EF?
Correct answer: D
The scale factor from ABC to DEF is 10 ÷ 8 = 1.25, so EF = 12 × 1.25 = 15 cm. 14 cm adds 2 cm, as if the sides grew by the same amount instead of the same factor.
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Question 8
A dilation centered at the origin maps the point (4, −6) to (10, −15). What is the scale factor?
Correct answer: D
10 ÷ 4 = 2.5 and −15 ÷ (−6) = 2.5, so the scale factor is 2.5. 0.4 divides the original by the image, and 6 is the difference 10 − 4.
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Question 9
Figure A is dilated by a scale factor of 2 and then translated 3 units to the right. Which statement is true about the final image and Figure A?
Correct answer: A
A dilation followed by a translation keeps the shape and all angles, so the figures are similar. The dilation doubled every length, so they are not congruent.
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Question 10
A triangle with an area of 10 cm² is dilated by a scale factor of 3. What is the area of the image?
Correct answer: B
Both the base and the height are multiplied by 3, so the area is multiplied by 3 × 3 = 9: 10 × 9 = 90 cm². 30 cm² multiplies the area by only 3.
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