Geometry Translations, Reflections and Rotations Test Solutions and Scoring (PDF)

\(A^{\prime}(2, -4),\ B^{\prime}(5, -4),\ C^{\prime}(3, -1)\)

A′(2, -4), B′(5, -4), C′(3, -1)

Scoring: 1 point for correct use of the rule, 1 point for all three vertices correct (deduct 1 if one is wrong).

1. \((-5, -2)\)
2. \((2, -5)\)

(a) (-5, -2); (b) (2, -5)

Scoring: 1 point per part.

1. \((-7, 3)\)
2. \((-3, -7)\)
3. \((7, -3)\)

(a) (-7, 3); (b) (-3, -7); (c) (7, -3)

Scoring: 1 point per part.

\(3 – (-2) = 5\) and \(1 – 6 = -5\), so the rule is \((x, y) \text{ maps to } (x + 5, y – 5)\).

\(L^{\prime} = (5, -5)\)

(x + 5, y − 5); L′(5, −5)

Scoring: 1 point for the rule, 1 point for L′.

Each coordinate changes sign: \((1, 1) \text{ maps to } (-1, -1)\) and \((4, 3) \text{ maps to } (-4, -3)\). This is \((x, y) \text{ maps to } (-x, -y)\).

A rotation of 180° about the origin

Scoring: 1 point for the correct name, 1 point for justification using the coordinates.

\((4, -2) \text{ maps to } (-4, -2) \text{ maps to } (-3, 4)\)

(-3, 4)

Scoring: 1 point for the reflection, 1 point for the translation.

First student: \((2, 1) \text{ maps to } (-1, 2) \text{ maps to } (-1, -2)\).

Second student: \((2, 1) \text{ maps to } (2, -1) \text{ maps to } (1, 2)\).

No, the images (-1, -2) and (1, 2) are different

Scoring: 1 point for each correct image, deduct nothing for a correct conclusion but state it.

The image has P′Q′ = 5, Q′R′ = 12 and m∠Q′ = 90°.

Reflections and translations are rigid motions, so they preserve distance and angle measure.

Scoring: 1 point for the three values, 1 point for the reason.

The point is 4 units from the line, so P′ is 4 units on the other side: \(3 – 4 = -1\). So P′ = (-1, 4).

The distance between the point and P′ is \(7 – (-1) = 8\).

P′(-1, 4); distance 8

Scoring: 1 point for the x-coordinate, 1 point for the full point, 1 point for the distance.