This geometry rigid transformations test answer key gives the full solution and the scoring guide for each of the 9 test questions on rigid transformations.
This answer key gives complete solutions and a point-by-point scoring guide for the rigid transformations test. Accept any valid sequence for the open-ended questions and award partial credit as described.
Geometry Rigid Transformations Test Answer Key: questions 1–5
Question 1: Translate a triangle (2 points)
Subtract 4 from each x-coordinate and add 3 to each y-coordinate.
\(A^{\prime}(-2,\,0)\), \(B^{\prime}(2,\,0)\), \(C^{\prime}(-1,\,2)\).
Scoring: 2 points if all three vertices are correct; 1 point if two are correct.
Question 2: Reflect over y = x (2 points)
Reflection over \(y=x\) swaps the coordinates of each point.
\(J^{\prime}(-4,\,1)\), \(K^{\prime}(-1,\,1)\), \(L^{\prime}(-4,\,4)\).
Scoring: 2 points if all three are correct; 1 point if two are correct.
Question 3: Rotate clockwise (2 points)
A \(90^{\circ}\) clockwise rotation sends \((x,\,y)\) to \((y,\,-x)\).
- \((2,\,-3)\)
- \((5,\,4)\)
- \((-6,\,0)\)
Scoring: 1 point for two correct images; 2 points for all three.
Question 4: Sequence of transformations (3 points)
- Reflection over the y-axis: \(D^{\prime}(-1,\,2)\), \(E^{\prime}(-4,\,2)\), \(F^{\prime}(-1,\,6)\). Translation: \(D^{\prime\prime}(1,\,-1)\), \(E^{\prime\prime}(-2,\,-1)\), \(F^{\prime\prime}(1,\,3)\).
- \(DE=4-1=3\) and \(D^{\prime\prime}E^{\prime\prime}=1-(-2)=3\). The lengths are equal, as expected for rigid transformations.
Scoring: Part (a): 1 point for the correct intermediate image, 1 point for the final image. Part (b): 1 point for both lengths.
Question 5: Identify the transformation (2 points)
Each point \((x,\,y)\) goes to \((-x,\,-y)\), for example \(A(1,\,1)\) to \(A^{\prime}(-1,\,-1)\).
The transformation is a rotation of \(180^{\circ}\) about the origin.
Scoring: 1 point for naming a rotation (a reflection over both axes in turn is also accepted); 1 point for the angle \(180^{\circ}\) and the center at the origin.
Geometry Rigid Transformations Test Answer Key: questions 6–9
Question 6: Rigid or not rigid (2 points)
- \(AB=4-1=3\). The image endpoints are \(A^{\prime}(1,\,3)\) and \(B^{\prime}(1,\,12)\), so \(A^{\prime}B^{\prime}=12-3=9\).
- No. The length changed from 3 to 9, and rigid transformations preserve length.
Scoring: 1 point for both lengths; 1 point for the conclusion with the reason.
Question 7: Symmetry (3 points)
- 8 lines: a regular polygon with \(n\) sides has \(n\) lines.
- \(360 : 8=45\): \(45^{\circ}\).
- 2 lines, one through the midpoints of each pair of opposite sides.
Scoring: 1 point per correct part.
Question 8: Describe a sequence (2 points)
One answer: rotate \(180^{\circ}\) about the origin, then translate by \(\langle -1,\,4\rangle\).
Rotation: \(A^{\prime}(6,\,-1)\), \(B^{\prime}(2,\,-1)\), \(C^{\prime}(2,\,-3)\), \(D^{\prime}(6,\,-3)\). Translation: \(A^{\prime\prime}(5,\,3)\), \(B^{\prime\prime}(1,\,3)\), \(C^{\prime\prime}(1,\,1)\), \(D^{\prime\prime}(5,\,1)\), which match the image.
Scoring: 1 point for a correct first transformation; 1 point for a second transformation that completes the mapping. Other valid sequences earn full credit.
Question 9: Robot position (2 points)
Reflection over the x-axis: \((-3,\,4)\) becomes \((-3,\,-4)\).
Translation: \((-3+5,\,-4+2)\) = \((2,\,-2)\).
Scoring: 1 point for the reflected point; 1 point for the final position.
Scoring summary
20 points: add the points of every question of this geometry rigid transformations test answer key.
How to use this geometry rigid transformations test answer key
Use this geometry rigid transformations test answer key to score the test fairly and to see which skills need more practice.
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