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 points 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 M? Please provide your answers in coordinate form with no spaces."

Answer 1

To reflect points across a vertical line, keep the y-coordinate the same and change the x-coordinate to its opposite.

Step-by-step explanation:

The equation of line M is x = -5, which means that all points on line M have an x-coordinate of -5. To reflect a point across line M, we need to keep the y-coordinate the same and change the x-coordinate to its opposite. Let's find the coordinates of the vertices of triangle A’B’C’ by reflecting points A, B, and C across line M:

A' has the same y-coordinate as A (-3) and its x-coordinate is -(-5) = 5. So, the coordinates of A' are (5, -3).

B' has the same y-coordinate as B (4) and its x-coordinate is -(-5) = 5. So, the coordinates of B' are (5, 4).

C' has the same y-coordinate as C (-5) and its x-coordinate is -(-5) = 5. So, the coordinates of C' are (5, -5).

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