Transformations Test – Grade 8 Math (Printable PDF)

Question 1 Points on the plane (2 points)

Point M is at (−3, 5).

1. Translate M by 6 units right and 8 units down. (1 point)
2. Reflect M across the x-axis. (1 point)

Question 2 Rotations of a point (3 points)

Point N is at (4, −6). Find its image after each rotation about the origin.

1. 90° counterclockwise (1 point)
2. 180° (1 point)
3. 270° counterclockwise (1 point)

Question 3 Identify the motion (3 points)

The figure shows △ABC and its image △A′B′C′.

1. Name the transformation. (1 point)
2. Write a coordinate rule for it. (1 point)
3. State two properties that are the same in both triangles. (1 point)

Question 4 Rigid motion properties (2 points)

A triangle with side lengths 6 in., 8 in., and 10 in. is rotated 90° about the origin.

1. Give the side lengths and the largest angle measure of the image. (1 point)
2. Is the image congruent to the original triangle? Explain. (1 point)

Question 5 Two moves on a quadrilateral (3 points)

Quadrilateral PQRS is shown. It is reflected across the x-axis and then translated 7 units right and 3 units up.

1. Find the vertices after the reflection. (1 point)
2. Find the vertices of the final image. (2 points)

Question 6 Find the rule (2 points)

Under one transformation, (−3, 4) maps to (3, −4) and (5, −1) maps to (−5, 1). Name the transformation and write its rule.

Question 7 Does order matter? (2 points)

Point (−2, 5) goes through two programs. Program A: rotate 90° counterclockwise about the origin, then translate 4 units right. Program B: translate 4 units right, then rotate 90° counterclockwise about the origin. Find both final points.

Question 8 Robotics mat (3 points)

A robotics club mat uses coordinates in feet. A robot starts at (−5, 3). Its program reflects the position across the y-axis, rotates it 180° about the origin, and then translates it 4 feet right and 6 feet down.

1. Find the robot’s final position. (2 points)
2. The first two steps together equal one reflection. Name it. (1 point)