Question

A sequence of transformations maps triangle ABC to triangle A’B’C’. The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the

- y-axis
- x-axis
- line y=x
OR - line y=-x

...followed by a translation

- 4 units to the right and 10 units up
- 8 units to the right and 10 units up
- 10 units to the right and 2 units up
OR - 10 units to the right and 4 units up.

Answer 1

Reflection across the line y=x followed by translation 10 units to the right and 4 units up.

Explanation:

Triangle ABC has vertices at points A(-6,2), B(-2,6) and C(-4,2).

1. The reflection across the line y=x has the rule

(x,y)→(y,x).

Thus,

• A(-6,2)→A''(2,-6);
• B(-2,6)→B''(6,-2);
• C(-4,2)→C''(2,-4).

2. The translation 10 units to the right and 4 units up has the rule

(x,y)→(x+10,y+4).

Thus,

• A''(2,-6)→A'(12,-2);
• B''(6,-2)→B'(16,2);
• C''(2,-4)→C'(12,0).

Points A'B'C' are exactly the vertices of the triangle A'B'C'.