Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Early problems dilate points and find scale factors. Later problems combine dilations with translations, scale models and a proof of AA similarity.
Standards: G-SRT.A.1, G-SRT.A.2, G-SRT.A.3 · Level: Grade 10 Geometry
Problem 2 Shrink a point ★★★
Dilate B(8, −6) about the origin with scale factor ½. Find B′.
Problem 3 Find the scale factor ★★★
A dilation about the origin maps P(4, 6) to P′(10, 15). Find the scale factor and verify it with both coordinates.
Problem 4 Length under a dilation ★★★
Segment AB is 7 centimeters long. Find the length of its image under a dilation with scale factor (a) 4 and (b) ½.
Problem 5 Distances from the center ★★★
The center of a dilation is C, and CP = 6. The scale factor is 2.5. Find CP′. If another dilation sends P to a point P″ with CP″ = 9, find its scale factor.
Problem 6 Dilate a triangle ★★★
Triangle ABC has A(1, 1), B(4, 1) and C(4, 3). Dilate it about the origin with k = 2. Find the image vertices, and compare the perimeters.
Problem 7 Dilation about another center ★★★
Dilate P(5, 4) about the center C(2, 1) with scale factor 2. Find P′.
Problem 8 A line not through the center ★★★
The line y = 2x + 3 is dilated about the origin with scale factor 3. Find the image of the points (0, 3) and (1, 5), and the equation of the image line. Compare it with the original line.
Problem 9 A line through the center ★★★
The line y = 3x passes through the origin. Dilate the point (1, 3) about the origin with scale factor 4. Show that the image is on the same line.
Problem 10 Perimeter and area ★★★
A triangle has perimeter 20 and area 15. It is dilated with scale factor 4. Find the perimeter and the area of the image.
Problem 11 Write the similarity statement ★★★
△ABC has m∠A = 52° and m∠B = 61°. △DEF has m∠D = 52° and m∠E = 67°. Are the triangles similar? If so, write the similarity statement with matching vertices.
Problem 12 Proportional sides ★★★
△ABC ∼ △DEF, with AB = 6, BC = 9 and DE = 10. Find the scale factor from △ABC to △DEF and the length of EF.
Problem 13 Is it a dilation ★★★
The rule (x, y) → (2x + 1, 2y) is applied to the points (0, 0) and (3, 0). Is this a dilation about the origin? Describe the transformation.
Problem 14 A similarity sequence ★★★
Triangle ABC has A(0, 0), B(2, 0) and C(0, 3). Triangle A′B′C′ has A′(4, 1), B′(8, 1) and C′(4, 7). Describe a dilation followed by a translation that maps one onto the other.
Problem 15 Scale model of a statue ★★★
A scale model of a statue is 18 centimeters tall. The real statue is 4.5 meters tall. Find the scale factor from the statue to the model. The statue’s base is 120 centimeters wide. How wide is the model’s base? By what factor is the surface area of the model smaller than the statue’s?
Problem 16 Projector enlargement ★★★
A slide measures 3.5 centimeters by 2.4 centimeters. A projector enlarges it with scale factor 18. Find the dimensions and the area of the image on the screen, and the factor by which the area grew.
Problem 17 Resizing a photo ★★★
A photo is 8 inches wide and 10 inches tall. It is shrunk by a dilation so that its width becomes 5 inches. Find the scale factor, the new height and the new perimeter.
Problem 18 Dilation with a center off the origin ★★★
Dilate A(2, 0) and B(4, 1) about the center (1, −2) with scale factor 3. Find A′ and B′, and compare the lengths AB and A′B′.
Problem 19 Prove the AA similarity ★★★
Given: In △ABC and △DEF, ∠A ≅ ∠D and ∠B ≅ ∠E. Prove that △ABC ∼ △DEF by showing a dilation and a rigid motion map △ABC onto △DEF.
Problem 20 Shadow measurement ★★★
A person who is 1.7 meters tall casts a shadow of 2.55 meters. At the same moment a tree casts a shadow of 12 meters. Explain why the triangles are similar and find the height of the tree.
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