← Back to the Transformations worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.G.A.1, 8.G.A.3 · Level: Grade 8
Problem 2 Reflect over the x-axis
The rule is (x, y) → (x, −y).
Image: (−4, −6)
Problem 3 Reflect over the y-axis
The rule is (x, y) → (−x, y).
Image: (−7, −3)
Problem 4 Quarter turn
The rule is (x, y) → (−y, x), so (7, 3) → (−3, 7).
Image: (−3, 7)
Problem 5 Half turn
The rule is (x, y) → (−x, −y).
Image: (6, −1)
Problem 6 Translate a triangle
Apply the rule to each vertex: J(1, −2) → (−3, 4); K(5, −2) → (1, 4); L(3, 1) → (−1, 7).
Image: J′(−3, 4), K′(1, 4), L′(−1, 7)
Problem 7 Mirror a quadrilateral
Change the sign of each x-coordinate: A(2, 1) → (−2, 1); B(6, 1) → (−6, 1); C(5, 4) → (−5, 4); D(3, 5) → (−3, 5).
Image: A′(−2, 1), B′(−6, 1), C′(−5, 4), D′(−3, 5)
Problem 8 Three-quarter turn
The rule is (x, y) → (y, −x), so (4, −3) → (−3, −4).
Check: a 90° counterclockwise turn gives (3, 4), and three such turns give the same result as turning 270°.
Image: (−3, −4)
Problem 9 Clockwise turn
A 90° clockwise rotation equals a 270° counterclockwise rotation, with rule (x, y) → (y, −x).
(−5, 2) → (2, 5).
Image: (2, 5)
Problem 10 Name the reflection
Each x-coordinate stays the same and each y-coordinate changes sign.
Reflection across the x-axis; (x, y) → (x, −y)
Problem 11 Name the rotation
Test (x, y) → (−y, x): P(1, 4) → (−4, 1) and Q(3, −2) → (2, 3). Both match.
Rotation of 90° counterclockwise about the origin; (x, y) → (−y, x)
Problem 12 What stays the same?
A reflection is a rigid motion, so lengths and angle measures are preserved.
Sides: 7 cm, 9 cm, 12 cm; the angle is 48°
Problem 13 Describe the slide
Compare X(−6, 3) with X′(1, −1): the x-coordinate increases by 7 and the y-coordinate decreases by 4. Y and Z follow the same change.
7 units right and 4 units down; (x, y) → (x + 7, y − 4)
Problem 14 Parallel lines survive
Slope of m: (4 − 1) ÷ (2 − 0) = 3/2. Slope of n: (3 − 0) ÷ (5 − 3) = 3/2, so the lines are parallel.
Image points: (0, −1) and (2, −4) for m′; (3, 0) and (5, −3) for n′.
Slope of m′: (−4 − (−1)) ÷ 2 = −3/2. Slope of n′: (−3 − 0) ÷ 2 = −3/2.
Both image lines have slope −3/2, so they are parallel.
Problem 15 Robot on a grid
East adds to x; south subtracts from y: (−4 + 7, 3 − 5) = (3, −2).
Reflect across the y-axis: (3, −2) → (−3, −2).
The robot ends at (−3, −2).
Problem 16 Order matters
Program 1: (2, 3) → (−2, 3) → (−3, −2).
Program 2: (2, 3) → (−3, 2) → (3, 2).
The final points (−3, −2) and (3, 2) are different, so the order matters.
Problem 17 Sprite in motion
Rotate 180°: S(−2, 1) → (2, −1); T(−5, 1) → (5, −1); U(−2, 4) → (2, −4).
Slide (x − 3, y + 5): (2, −1) → (−1, 4); (5, −1) → (2, 4); (2, −4) → (−1, 1).
Final image: S″(−1, 4), T″(2, 4), U″(−1, 1)
Problem 18 Table turn
Rule (x, y) → (−y, x): (1, 2) → (−2, 1); (5, 2) → (−2, 5); (5, 4) → (−4, 5); (1, 4) → (−4, 1).
Original: 4 by 2, area 8. Image: width from −4 to −2 is 2, height from 1 to 5 is 4, area 2 · 4 = 8.
New corners (−2, 1), (−2, 5), (−4, 5), (−4, 1); area 8 square units in both
Problem 19 Logo in three steps
Rotate: (2, 2) → (−2, 2); (6, 3) → (−3, 6); (3, 6) → (−6, 3).
Reflect across the x-axis: (−2, −2); (−3, −6); (−6, −3).
Translate (x + 2, y − 1): (0, −3); (−1, −7); (−4, −4).
Final vertices (0, −3), (−1, −7), (−4, −4)
Problem 20 Two mirrors, one turn
(6, −1) → (6, 1) → (−6, 1). (−7, 2) → (−7, −2) → (7, −2).
The rule overall is (x, y) → (−x, −y), which is the 180° rotation: (6, −1) → (−6, 1) and (−7, 2) → (7, −2).
A 180° rotation about the origin