Transformations and Congruence: math test solutions, Grade 8 – download the PDF

1 Translation / 4 pts

1. \(A'(3,\,-2)\), \(B'(6,\,-2)\), \(C'(3,\,2)\) (3 pts).
2. \(AC=5-1=4\) and \(A'C'=2-(-2)=4\). Translations preserve lengths (1 pt).

2 Reflections / 3 pts

(a) \((-6,\,2)\) (1 pt). (b) \((6,\,-2)\) (1 pt).

(c) \(M\) is 6 units from the y-axis and so is its image \((6,\,-2)\) (1 pt).

3 Rotations / 4 pts

(a) \((-4,\,3)\) (1 pt). (b) \((-3,\,-4)\) (1 pt). (c) \((4,\,-3)\) (1 pt).

(d) \(\sqrt{16+9}=5\), \(\sqrt{9+16}=5\), \(\sqrt{16+9}=5\), and \(P\) itself: \(\sqrt{9+16}=5\) (1 pt).

4 True or false? / 3 pts

1. False: rotations are rigid and preserve angles (1 pt).
2. True: same size and same shape, so a rigid motion maps one onto the other (1 pt).
3. False: a 6 cm by 4 cm rectangle and a 7 cm by 3 cm rectangle both have perimeter 20 cm but different side lengths (1 pt).

5 A sequence of transformations / 4 pts

1. Reflection: \((1,\,-2)\), \((4,\,-2)\), \((1,\,-6)\). Translation: \(D_2(-1,\,1)\), \(E_2(2,\,1)\), \(F_2(-1,\,-3)\) (3 pts).
2. The final triangle is congruent to \(DEF\), so its perimeter is \(3+4+5=12\) units (1 pt).

6 Game sprite / 2 pts

After the reflection: \((-2,\,8)\) (1 pt). After moving down: \((-2,\,3)\) (1 pt).