Question

What are the coordinates of the image of point L(4, 2) after a reflection over the line y = –1?

(4, –4)

(4, –2)

(–5, 2)

(3, 1)

Answer 1

L'(4, -4)

Explanation:

When you're given a midpoint, you can find the point equidistant on the other side of the midpoint by subtracting the relevant coordinate from double that of the midpoint.

Here, the line of reflection is the horizontal line y=-1, so you know only the y-coordinate will change. The reflected point will be ...

(x, y) ⇒ (x, -2-y)

so the point of interest is ...

L' = (4, -2-2) = (4, -4)