1. There are two triangles, ΔQRS and ΔABC. The coordinates of ΔQRS are Q(−3, 3), R(−6, 3), and S(−3, 8). The coordinates of ΔABC are A(0, −3), B(0, −6), and C(5, −3).
Which of the following is a description of rigid motions which map ΔQRS to ΔABC?
A. A rotation of 90° about the origin, followed by a translation 3 units to the left and then a reflection across the y-axis
B. A rotation of 90° about the origin, followed by a translation 4 units to the right and then a reflection across the x-axis
C. A rotation of 90° about the origin, followed by a translation 3 units to the right and then a reflection across the y-axis
2. ΔEFG and ΔHIJ are congruent triangles. The coordinates of ΔEFG are E(5, 4), F(7, 4), and G(7, 8). The coordinates of HI are H(0, 0), and I(0, 2).
a. What are possible coordinates of point J?
A. (–3, 2)
B. (–5, 2)
C. (–4, 2)
D. (–6, 2)
b. Explain why there can be different possibilities for the coordinates for point J.
3. On a math test Nikol needs to describe the motions which map ΔEFG to ΔMNO. The coordinates of ΔEFG are E(4, 5), F(6, 5), and G(4, 10). The coordinates of ΔMNO are M(0, 0), N(–2, 0), and O(0, 5). She says there is a translation 4 units to the left and 5 units down, followed by a reflection across the x-axis.
a. Write a description of the rigid motions which maps ΔEFG to ΔMNO.
b. What is Nikol's likely error?
4. The coordinates of the figure ABCD are A(6, 2), B(8, 2), C(8, 6), and D(6, 6). The coordinates of the figure HIJK are H(−1, 0), I(−1, −2), J(−5, −2), and K(−5, 0).
a. Write a description of rigid motions used.
b. Describe a different sequence of rigid motions that will still map ABCD to HIJK.