Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Draw a quick sketch whenever a problem gives coordinates, and check each image against the figure before writing the final answer.
Standards: 8.G.A.1, 8.G.A.3 · Level: Grade 8
Problem 1 Slide a point ★★★
Translate the point (6, −7) by 9 units to the right and 3 units up. Write the image.
Problem 2 Reflect over the x-axis ★★★
Reflect the point (−4, 6) across the x-axis.
Problem 3 Reflect over the y-axis ★★★
Reflect the point (7, −3) across the y-axis.
Problem 4 Quarter turn ★★★
Rotate the point (7, 3) by 90° counterclockwise about the origin.
Problem 5 Half turn ★★★
Rotate the point (−6, 1) by 180° about the origin.
Problem 6 Translate a triangle ★★★
Triangle JKL is shown. Apply the rule (x, y) → (x − 4, y + 6) and list the vertices of △J′K′L′.
Problem 7 Mirror a quadrilateral ★★★
Reflect quadrilateral ABCD across the y-axis. Write the coordinates of each image vertex.
Problem 8 Three-quarter turn ★★★
Rotate the point (4, −3) by 270° counterclockwise about the origin.
Problem 9 Clockwise turn ★★★
Rotate the point (−5, 2) by 90° clockwise about the origin.
Problem 10 Name the reflection ★★★
Points A(2, 3) and B(−4, 1) are mapped to A′(2, −3) and B′(−4, −1). Name the transformation and write its rule.
Problem 11 Name the rotation ★★★
Points P(1, 4) and Q(3, −2) are mapped to P′(−4, 1) and Q′(2, 3). Name the transformation and write its rule.
Problem 12 What stays the same? ★★★
A triangle has sides 7 cm, 9 cm, and 12 cm, and one angle of 48°. The triangle is reflected across the y-axis. Give the three side lengths and that angle measure in the image.
Problem 13 Describe the slide ★★★
The figure shows △XYZ and its image. Describe the translation in words and write the rule.
Problem 14 Parallel lines survive ★★★
Line m passes through (0, 1) and (2, 4). Line n passes through (3, 0) and (5, 3). Reflect both lines across the x-axis. Show that the image lines are parallel.
Problem 15 Robot on a grid ★★★
A cleaning robot starts at (−4, 3) on a floor map measured in feet. It drives 7 feet east and 5 feet south. A mirror program then reflects its position across the y-axis. Where does the robot end up?
Problem 16 Order matters ★★★
A game designer tests two programs on the point (2, 3). Program 1: reflect across the y-axis, then rotate 90° counterclockwise about the origin. Program 2: rotate 90° counterclockwise first, then reflect across the y-axis. Find both final points. Are they the same?
Problem 17 Sprite in motion ★★★
In a video game, sprite △STU rotates 180° about the origin and then slides 3 units left and 5 units up. Find the coordinates of the final image △S″T″U″.
Problem 18 Table turn ★★★
A rectangular table in a school cafeteria plan has corners (1, 2), (5, 2), (5, 4), and (1, 4). The plan is rotated 90° counterclockwise about the origin. Find the new corners. Then show that the area is unchanged.
Problem 19 Logo in three steps ★★★
A logo pennant has vertices (2, 2), (6, 3), and (3, 6). Rotate it 90° counterclockwise about the origin, reflect the result across the x-axis, then translate it 2 units right and 1 unit down. Find the final vertices.
Problem 20 Two mirrors, one turn ★★★
Reflect the points (6, −1) and (−7, 2) across the x-axis, and then reflect each result across the y-axis. Which single rotation about the origin gives the same result? Explain.
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