Testinar Grade 8 math

Rotations, Reflections, and Translations

Learn to reason about and solve Grade 8 problems involving Rotations, Reflections, and Translations.

CH05-01 Geometry and Measurement

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Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Looking at the two rectangles, which transformation was applied?
1. Reflection across the \(x\)-axis
2. Reflection across the \(y\)-axis
3. 180° rotation about the origin
4. Dilation by scale factor \(2\)
The triangle was reflected across which line?
1. \(y = x\)
2. \(y = -x\)
3. The \(y\)-axis
4. The line \(y = 2\)
The figure shows shape A and shape B. Which single transformation maps A to B?
1. Reflection across the \(y\)-axis
2. Translation 4 units right
3. Rotation 90° counterclockwise
4. Dilation with scale factor \(2\)
Which sequence of transformations was applied?
1. Translate 5 units down, then rotate 90°
2. Reflect across the \(x\)-axis, then rotate
3. Rotate 90° counterclockwise, then translate 5 units down
4. Dilate by scale factor 2, then translate
The blue rectangle is transformed to the dashed red rectangle. Which line of reflection was used?
1. The \(x\)-axis
2. The \(y\)-axis
3. The line \(y = -x\)
4. The origin point \((0,0)\)
If Shape C is rotated 180° about the origin, which shape results?
1. Shape D
2. The same shape (unchanged)
3. A shape in Quadrant II
4. A shape above the \(x\)-axis in Quadrant II
The figure shows a transformation. If this is a reflection across the \(x\)-axis, which vertex of the pre-image corresponds to the vertex at \((3,-1)\) in the image?
1. \((1, 1)\)
2. \((3, 1)\)
3. \((4, 3)\)
4. \((2, 3)\)
Figures E and F are congruent. If Figure E was transformed to Figure F, which transformation(s) could have been applied?
1. Only a translation
2. Only a reflection
3. A reflection and a translation
4. A rotation and a dilation

Teacher and parent reference

Answer key and explanations

C. 180° rotation about the origin
A 180° rotation about the origin maps \((x, y) \to (-x, -y)\). The pre-image at \((1,1)\) maps to \((-1,-1)\) in the image, confirming the rotation.
C. The \(y\)-axis
Reflecting across the \(y\)-axis changes \((x, y) \to (-x, y)\). The pre-image vertex \((3,2) \to (-3,2)\) and apex \((2,0) \to (-2,0)\), matching the image.
B. Translation 4 units right
Shape A has a corner at \((-2, 1)\) and shape B has a corresponding corner at \((2, 1)\). The horizontal shift is \(2 - (-2) = 4\) units.
C. Rotate 90° counterclockwise, then translate 5 units down
A 90° counterclockwise rotation sends the rectangle to a vertical position. Translating that rotated image 5 units down matches the orange image.
C. The line \(y = -x\)
Reflection across \(y = -x\) maps \((x,y) \to (-y, -x)\). The point \((1,2)\) maps to \((-2, -1)\) in the image.
A. Shape D
A 180° rotation about the origin takes a point in Quadrant I to Quadrant III. Shape C's corner at \((2,3)\) maps to \((-2,-3)\), matching Shape D.
B. \((3, 1)\)
Reflection across the \(x\)-axis uses \((x, y) \to (x, -y)\). The point \((3,1)\) reflects to \((3,-1)\).
A. Only a translation
Figure E and Figure F have the same size and orientation. Each point moves 5 units left and 1 unit up (translation), not a rotation which would change orientation.