Question

Suppose M is the line with equation x = -5, line N is the line with equation y = 1, line G is the line with equation y = x, and line H is the line with equation y = -2. Given A(9, -3), B(6, 4), and C(-1, -5), what are the coordinates of the vertices of triangle A'B'C' for a reflection across line G?

(a) A'(3, 9), B'(4, 6), C'(5, -1)
(b) A'(-3, 9), B'(-4, 6), C'(-5, -1)
(c) A'(3, -9), B'(4, -6), C'(5, 1)
(d) A'(-3, -9), B'(-4, -6), C'(-5, 1)

Answer 1

The triangle's vertices after reflection across the line y = x are A'(-3, 9), B'(-4, 6), C'(-5, -1), matching option (b).

Step-by-step explanation:

The question concerns finding the coordinates of the vertices of a triangle after a reflection across the line y = x. To reflect a point across the line y = x, you swap the x and y coordinates of the point. Let's apply this to each point.

• A(9, -3) becomes A'(x', y') where x' = -3 and y' = 9. Hence A'(-3, 9).
• B(6, 4) becomes B'(x', y') where x' = 4 and y' = 6. Thus B'(-4, 6).
• C(-1, -5) becomes C'(x', y') where x' = -5 and y' = -1. Therefore C'(-5, -1).

The correct answer is (b) A'(-3, 9), B'(-4, 6), C'(-5, -1).