Question

the point g(-5, -1) is reflected over the line y = -3. what are the coordinates of the resulting point, g?

Explanation:

Step1: Find the distance between the y - coordinate of G and the line y = - 3.

The y - coordinate of point G is - 1, and the line is y=-3. The distance \(d\) between - 1 and - 3 is \(|-1-(-3)|=|-1 + 3|=2\).

Step2: Determine the y - coordinate of \(G'\).

Since we are reflecting over the line \(y = - 3\), the y - coordinate of \(G'\) will be at a distance of 2 from \(y=-3\) on the opposite side of G. So we subtract 2 from - 3 (because we are moving down from the line \(y=-3\) by the same distance as we were above). So the y - coordinate of \(G'\) is \(-3-2=-5\). The x - coordinate remains the same because we are reflecting over a horizontal line, so the x - coordinate of \(G'\) is - 5.

Answer:

\((-5,-5)\)