Practice Geometric Transformation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A function that maps every point of a geometric figure to a new position, changing its location, orientation, or size.

Moving, rotating, flipping, or stretching a shape to produce a new image of that shape.

Showing a random 20 of 50 problems.

Example 1

medium
A figure is dilated by factor 3. Is the image congruent or similar to the original?

Example 2

easy
Translate (0,0)(0,0) by the vector ⟨−3,7⟩\langle -3,7\rangle.

Example 3

hard
After a dilation by factor −2-2 about the origin, where does (3,5)(3,5) map?

Example 4

easy
Which three transformations are 'rigid' (preserve size and shape)?

Example 5

easy
A figure is flipped over a line. What transformation is this?

Example 6

medium
Compose two reflections across parallel lines ℓ1:x=0\ell_1: x=0 and ℓ2:x=3\ell_2: x=3. What is the result?

Example 7

medium
A figure is translated, then rotated. Is the final image congruent to the original?

Example 8

hard
A triangle has area 1212 and perimeter 2020. After dilation by factor 55, what are the new area and perimeter?

Example 9

easy
Name and describe the four basic geometric transformations.

Example 10

medium
Rotate (4,1)(4,1) by 90°90° CCW, then translate by ⟨2,−3⟩\langle 2,-3\rangle. Find the final image.

Example 11

easy
Apply (x,y)↦(x+4,y−2)(x,y)\mapsto(x+4,y-2) to the point (3,5)(3,5).

Example 12

easy
Which transformation changes a figure's size: translation or dilation?

Example 13

medium
Point P(3,−1)P(3, -1) is reflected over the y-axis, then translated by (2,5)(2, 5). Find the final image.

Example 14

easy
After dilation by factor 14\tfrac{1}{4}, what happens to a length of 2020?

Example 15

easy
Reflect (4,9)(4,9) across the yy-axis.

Example 16

easy
Which geometric transformations are isometries (preserve distances)?

Example 17

hard
What is the image of (5,2)(5,2) under a reflection across the line y=xy=x, followed by a 90°90° CCW rotation about the origin?

Example 18

medium
Why does tracking only the vertices of a polygon suffice to transform the whole figure?

Example 19

hard
Two figures have areas 99 and 3636 and are similar. What is the ratio of their corresponding sides?

Example 20

easy
A transformation maps (x,y)→(x+2,y−3)(x, y) \to (x+2, y-3). What type is it?
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