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Grade 8 · unit review

Review: Rigid Transformations and Their Order

Translations, reflections and rotations preserve distances and angle measures. Coordinate rules describe these moves exactly, and a sequence of moves must be applied in its stated order to determine the final image.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Translate (-7,8) by vector (3,−2).
Need a hint?
  • A translation adds the same horizontal and vertical displacements to every point.
  • Add vector components to matching coordinates; do not multiply them or reverse signs without a reason.
2. Reflect (7,−8) across the y-axis.
Need a hint?
  • Reflection across the y-axis negates a point’s horizontal coordinate and leaves its vertical coordinate unchanged.
  • Negate x for a y-axis reflection, even though the axis name contains y.
3. Rotate (7,8) 90° counterclockwise about the origin.
Need a hint?
  • A ninety-degree counterclockwise rotation around the origin sends (x,y) to (−y,x).
  • Clockwise rotation uses a different rule.
4. Reflect (7,8) across the x-axis, then translate by (1,2).
Need a hint?
  • Composing transformations means applying each move to the result of the previous one.
  • The order is part of the instructions; these moves need not commute.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Translate (-9,10) by vector (3,−2). Candidate answers: (A) (-12,12) (B) (-27,-20) (C) (-6,12) (D) (-6,8). 2. Reflect (9,−10) across the y-axis. Candidate answers: (A) (9,10) (B) (−10,9) (C) (−9,10) (D) (−9,−10). 3. Rotate (9,10) 90° counterclockwise about the origin. Candidate answers: (A) (10,−9) (B) (9,−10) (C) (−10,9) (D) (−9,−10). 4. Reflect (9,10) across the x-axis, then translate by (1,2). Candidate answers: (A) (-8,12) (B) (10,-12) (C) (10,-8) (D) (10,12).

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. (-6,8). Add each component to the matching coordinate: (-9+3,10−2)=(-6,8). Translation preserves lengths and angle measures. 2. (−9,−10). A y-axis reflection negates x and keeps y. Points stay the same horizontal distance from the y-axis on the opposite side. 3. (−10,9). The 90° counterclockwise rule is (x,y)→(−y,x). It gives (−10,9); the distance from the origin is unchanged. 4. (10,-8). First obtain (9,−10); then add the translation to get (9+1,−10+2). Reversing the operations would generally produce a different point.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.