Question

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image?

Answer 1

ANSWER

The coordinates of the image are (2,2)

EXPLANATION

The mapping for a reflection across the line y=k is :

$(x,y)\to (x,2k-y)$

We want to find the image of the point (2,-4) after a reflection in the line y=-1.

In this case k=-1.

$(2, - 4)\to (2,2( - 1)- - 4)$

This simplifies to,

$(2, - 4)\to (2, - 2 + 4)$

$(2, - 4)\to (2, 2)$

Hence the image is (2,2)