8th Grade Dilations and Similar Figures Test Solutions and Scoring (PDF)

8th Grade math test solutions: Dilations and Similar Figures – Maths PDF

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This dilations similarity test answers for 8th Grade covers dilations and similar figures (Common Core 8.G.A.3, 8.G.A.4), with a free PDF to print.

Use this answer key to score the dilations and similar figures test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.G.A.3, 8.G.A.4

Dilations similarity test answers: worked solutions

Question 1 – Dilate points [2 pts]

\((12, -20)\)
\((3, 2)\)

Scoring: 1 point each.

Question 2 – Dilate a figure [3 pts]

The image doubles each coordinate.

\((x, y) \to (2x, 2y)\).

\(K^{\prime}(4, 2),\ L^{\prime}(8, 2),\ M^{\prime}(4, 10)\)

Scoring: 1 point for the rule. 2 points for three vertices.

Question 3 – Scale factor [2 pts]

Each side of the large triangle is 2 times the matching side.

\(k = \frac{6}{3} = 2\). Perimeter: \(12 \cdot 2 = 24\).

Scoring: 1 point for the scale factor. 1 point for the perimeter.

Question 4 – Missing length [3 pts]

\(k = \frac{15}{5} = 3\). \(HI = 7 \cdot 3 = 21\).

Scoring: 1 point for the scale factor, 1 point for matching sides, 1 point for 21.

Question 5 – Tree height [3 pts]

\(\frac{h}{5} = \frac{12}{3}\), so \(h = 5 \cdot 4 = 20\) feet.

Scoring: 1 point for the proportion. 1 point for solving. 1 point for 20 ft.

Question 6 – Area [2 pts]

Image side: 15 cm, area 225. Original area: 25. The area is 9 times as large.

Scoring: 1 point for 225. 1 point for the comparison.

Question 7 – Describe a sequence [3 pts]

Dilation with scale factor 3 gives \((3, 0)\), \((6, 0)\), \((3, 6)\). Reflection across the y-axis gives \((-3, 0)\), \((-6, 0)\), \((-3, 6)\).

Scoring: 1 point for the dilation, 1 point for the reflection, 1 point for order and checking.

Question 8 – Explain [2 pts]

Both have equal corresponding angles. Congruent figures also have equal lengths; similar figures have lengths in proportion.

Scoring: 1 point for angles. 1 point for lengths.

Total score

Total

20 points

Key facts behind this dilations similarity test answers

Key facts

Dilation from the origin: \((x, y) \to (kx, ky)\).
\(k > 1\) enlarges; \(0 < k < 1\) reduces; \(k = 1\) leaves the figure unchanged.
Angles stay equal; side lengths multiply by \(k\); area multiplies by \(k^{2}\).
Similar figures have equal angles and proportional sides.
Use \(\frac{\text{new}}{\text{old}} = k\) to find missing lengths.

How to use this dilations similarity test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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