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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.G.A.2, 8.G.A.3, 8.G.A.4 · Level: Grade 8
Problem 2 Shrink a point
Multiply both coordinates by 1/4: (28 ÷ 4, −20 ÷ 4).
Image: (7, −5)
Problem 3 Fractional factor
(−6 · 2/3, 9 · 2/3) = (−4, 6).
Image: (−4, 6)
Problem 4 Find the scale factor
Divide an image coordinate by the pre-image coordinate: 15 ÷ 6 = 2.5, and −10 ÷ (−4) = 2.5.
Scale factor: 2.5
Problem 5 Rectangle sizes
8 · 2.5 = 20 and 5 · 2.5 = 12.5.
Image: 20 cm by 12.5 cm
Problem 6 Double a triangle
Multiply each coordinate by 2: A(1, 2) → (2, 4); B(4, 1) → (8, 2); C(3, 4) → (6, 8).
Image: A′(2, 4), B′(8, 2), C′(6, 8)
Problem 7 Shrink a trapezoid
Halve every coordinate: D(2, 6) → (1, 3); E(8, 6) → (4, 3); F(8, 2) → (4, 1); G(4, 2) → (2, 1).
Image: D′(1, 3), E′(4, 3), F′(4, 1), G′(2, 1)
Problem 8 Show congruence
Reflect across the y-axis: A(−5, 1) → (5, 1); B(−1, 1) → (1, 1); C(−4, 4) → (4, 4).
Translate 5 units down: (5, −4), (1, −4), (4, −1), which are A′, B′, C′.
A reflection across the y-axis, then a translation 5 units down; the triangles are congruent
Problem 9 Check a dilation of sides
12 ÷ 9 = 4/3; 20 ÷ 15 = 4/3; 28 ÷ 21 = 4/3. All three ratios match.
The scale factor is 4/3, so the triangles are similar
Problem 10 Similar rectangles?
15 ÷ 10 = 3/2 and 21 ÷ 14 = 3/2. The ratios are equal, and all angles are 90°.
Yes; the scale factor from R to S is 3/2
Problem 11 Missing side
Scale factor: 6 ÷ 9 = 2/3.
12 · 2/3 = 8 and 15 · 2/3 = 10.
The other sides are 8 and 10.
Problem 12 Shrink to a third
Divide each coordinate by 3: (−3, 6) → (−1, 2); (9, −3) → (3, −1); (0, −6) → (0, −2).
Image: (−1, 2), (3, −1), (0, −2)
Problem 13 Reduce or enlarge?
4.5 ÷ 9 = 0.5; 6 ÷ 12 = 0.5; 7.5 ÷ 15 = 0.5.
Scale factor 1/2; the dilation reduces the triangle
Problem 14 Lengths scale too
A′ = (5, 7.5) and B′ = (15, 7.5).
AB = 6 − 2 = 4 and A′B′ = 15 − 5 = 10, and 10 ÷ 4 = 2.5.
A′(5, 7.5), B′(15, 7.5); A′B′ is 2.5 times AB
Problem 15 Similar by two moves
AB = 2 and DE = 4, AC = 1 and DF = 2, so k = 2. Dilate: A(1, 1) → (2, 2); B(3, 1) → (6, 2); C(1, 2) → (2, 4).
Translate 8 left and 5 down: (2, 2) → (−6, −3); (6, 2) → (−2, −3); (2, 4) → (−6, −1), which are D, E, F.
Dilation with k = 2, then a translation 8 units left and 5 units down
Problem 16 Poster enlargement
4 · 3.5 = 14 and 6 · 3.5 = 21.
Both dimensions are multiplied by the same factor and the angles stay 90°, so the shapes are similar.
Poster: 14 in. by 21 in.
Problem 17 Model airplane
36 m = 3,600 cm, so the scale factor is 24 ÷ 3,600 = 1/150.
31.5 m = 3,150 cm and 3,150 ÷ 150 = 21.
Scale factor 1/150; the model fuselage is 21 cm long
Problem 18 Shadow measurement
Scale factor from student shadow to tree shadow: 33 ÷ 8.25 = 4.
Heights are scaled the same way: 5.5 · 4 = 22.
The tree is 22 ft tall.
Problem 19 Garden map
Multiply by 1.5: (4, 2) → (6, 3); (10, 2) → (15, 3); (10, 10) → (15, 15).
Original sides: 6, 8, and √(36 + 64) = 10, perimeter 24 m. New sides: 9, 12, 15, perimeter 36 m, and 36 ÷ 24 = 1.5.
New vertices (6, 3), (15, 3), (15, 15); the perimeter grows from 24 m to 36 m, by the scale factor 1.5
Problem 20 Three moves
Dilate: (4, 4), (12, 4), (4, 10).
Reflect across the y-axis: (−4, 4), (−12, 4), (−4, 10).
Translate (x + 3, y − 1): (−1, 3), (−9, 3), (−1, 9).
The sides grow from 4, 3, 5 to 8, 6, 10, so the scale factor is 2, not 1.
Final vertices (−1, 3), (−9, 3), (−1, 9); similar but not congruent