Question

if $a(-2,5)$ is reflected in the line $y = 3$, what are the coordinates of $a$?

Explanation:

Step1: Calculate the distance from point A to the line y = 3

The y - coordinate of point A is 5 and the line is y = 3. The distance $d=|5 - 3|=2$.

Step2: Determine the y - coordinate of the reflected point

Since we are reflecting over the line y = 3, the x - coordinate of the point remains the same. The y - coordinate of the reflected point $y_1$ is found by moving the same distance on the other side of the line y = 3. So $y_1=3-(5 - 3)=1$. The x - coordinate of point A is - 2 and it stays - 2 for the reflected point.

Answer:

$(-2,1)$