This grade 8 transformations test answer key gives the full solution and the scoring guide for each of the 8 test questions on translations, reflections and rotations.
Use this key to score the transformations test out of 20 points. Each solution shows the work and how the points are awarded. Give partial credit for the correct rule even if one coordinate has an arithmetic slip.
Grade 8 Transformations Test Answer Key: questions 1–5
Question 1: Move a point (2 points)
(a) \((-3+5,\,4-6)=(2,-2)\).
(b) \((x,-y)\): \((-3,-4)\).
Scoring: 1 point for each correct image.
Question 2: Rotate a point (3 points)
(a) \((-y,x)=(5,2)\).
(b) \((-x,-y)=(-2,5)\).
(c) \((y,-x)=(-5,-2)\).
Scoring: 1 point for each correct image.
Question 3: Translate a triangle (3 points)
\(A^{\prime}(2,-1)\), \(B^{\prime}(6,-1)\), \(C^{\prime}(2,2)\).
Scoring: 1 point for each correct vertex.
Question 4: Reflect a triangle (3 points)
(a) \(D^{\prime}(-1,2)\), \(E^{\prime}(-5,2)\), \(F^{\prime}(-4,5)\).
(b) \(D^{\prime}(1,-2)\), \(E^{\prime}(5,-2)\), \(F^{\prime}(4,-5)\).
(c) Reflections keep lengths and angles: \(D^{\prime}E^{\prime}=4\) and \(\angle D^{\prime}=45^{\circ}\).
Scoring: 1 point for (a), 1 point for (b), 1 point for (c).
Question 5: Rotate a triangle (3 points)
Use \((x,y)\to(-y,x)\).
\(G^{\prime}(-1,2)\), \(H^{\prime}(-1,6)\), \(J^{\prime}(-4,2)\).
Scoring: 1 point for the rule used, 1 point for two correct vertices, 1 point for all three correct.
Grade 8 Transformations Test Answer Key: questions 6–8
Question 6: Name the motion (2 points)
Both coordinates changed sign: \((1,3)\to(-1,-3)\), \((4,3)\to(-4,-3)\), \((1,5)\to(-1,-5)\).
The motion is a rotation of \(180^{\circ}\) about the origin, \((x,y)\to(-x,-y)\).
Scoring: 1 point for the rotation of 180 degrees, 1 point for the rule.
Question 7: Properties of rigid motions (2 points)
A rotation keeps lengths and angle measures: \(A^{\prime}B^{\prime}=7\text{ in}\), \(B^{\prime}C^{\prime}=4\text{ in}\), \(\angle A^{\prime}=60^{\circ}\).
Rotations keep parallel lines parallel, and \(\overline{AB}\) is parallel to \(\overline{CD}\), so the images are parallel.
Scoring: 1 point for the two lengths and the angle, 1 point for parallel with the reason.
Question 8: Find the original point (2 points)
The rule is \((x,y)\to(y,-x)\). So \(y=4\) and \(-x=-7\), so \(x=7\).
Check: \((7,4)\to(4,-7)\).
The original point is \(S(7,4)\).
Scoring: 1 point for using the rule correctly, 1 point for S(7, 4).
Scoring summary
20 points: add the points of every question of this grade 8 transformations test answer key.
How to use this grade 8 transformations test answer key
Use this grade 8 transformations test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Grade 8 math page.