8th Grade Dilations and Similar Figures Worksheet Solutions (PDF)

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

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This dilations similarity 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.

This answer key gives a full worked solution for each of the 21 problems on the dilations and similar figures worksheet (Common Core 8.G.A.3 and 8.G.A.4). Compare each step with your own work, not only the final answer, and note any step where your method differed.

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

Dilations similarity answers: exercises 1 to 10

Exercise 1 – Dilate a point

Multiply each coordinate by 3.

\((6, 9)\)

Exercise 2 – Reduce a point

\(\frac{1}{2} \cdot 4 = 2\) and \(\frac{1}{2} \cdot (-6) = -3\).

\((2, -3)\)

Exercise 3 – Dilate a triangle

Each coordinate doubles.

\(A^{\prime}(2, 2),\ B^{\prime}(6, 2),\ C^{\prime}(2, 4)\)

Exercise 4 – Reduce a triangle

The image is half as large.

\(P^{\prime}(2, 1),\ Q^{\prime}(4, 1),\ R^{\prime}(2, 3)\)

Exercise 5 – Find the scale factor

\(k = \frac{6}{2} = 3\), and \(\frac{12}{4} = 3\).

\(k = 3\)

Exercise 6 – Enlargement or reduction

A factor less than 1 shrinks the figure; a factor greater than 1 enlarges it.

0.75: reduction; 1.5: enlargement

Exercise 7 – Side length

\(4 \cdot 3 = 12\).

Exercise 8 – Perimeter and area

Perimeter: \(12 \cdot 3 = 36\).

Area: \(6 \cdot 3^{2} = 54\).

Perimeter 36; area 54

Exercise 9 – Similar triangles

\(\frac{6}{3} = \frac{8}{4} = \frac{10}{5} = 2\).

Yes, similar with scale factor 2

Exercise 10 – Missing side

\(k = \frac{10}{4} = 2.5\). Length: \(6 \cdot 2.5 = 15\).

15 inches

Exercises 11 and up

Exercise 11 – Angles in similar triangles

Third angle of the first: \(180 – 50 – 60 = 70\). Similar triangles have equal corresponding angles.

50°, 60° and 70°

Exercise 12 – Scale factor 1

Each coordinate is multiplied by 1, so the image is the same figure.

The same figure; yes, congruent

Exercise 13 – Describe a sequence

Dilate with scale factor 2: \((2, 2)\), \((4, 2)\), \((2, 6)\). Then rotate \(180^{\circ}\) about the origin: \((-2, -2)\), \((-4, -2)\), \((-2, -6)\).

Dilation with k = 2, then a 180° rotation about the origin

Exercise 14 – Rectangle dilation

\(\frac{6}{4} = 1.5\) and \(\frac{3}{2} = 1.5\).

\(k = 1.5\)

Exercise 15 – Not similar

\(\frac{4}{2} = 2\) but \(\frac{7}{3} \approx 2.33\). The sides are not proportional.

No, not similar

Exercise 16 – Photo enlargement

\(4 \cdot 2.5 = 10\) and \(6 \cdot 2.5 = 15\).

10 inches by 15 inches

Exercise 17 – Shadow problem

\(\frac{h}{6} = \frac{10}{4}\), so \(h = 6 \cdot 2.5 = 15\).

The tree is 15 ft tall.

15 feet

Exercise 18 – Map scale

\(3.6 \cdot 25 = 90\) miles.

90 miles; each map inch is 25 real miles

Exercise 19 – Logo on a screen

\(k = \frac{12}{3} = 4\). Height: \(2 \cdot 4 = 8\).

Scale factor 4; height 8 cm

Exercise 20 – Poster area

Flyer: \(80\). Poster: \(24 \cdot 30 = 720\). \(720 \div 80 = 9 = 3^{2}\).

9 times as large

Exercise 21 – Explain

No. A dilation preserves angle measures. It only multiplies lengths by 2.

Noah is wrong

Key facts behind this dilations similarity 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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

All Grade 8 chapters: Grade 8 math.

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