Question

if e(-7, -5) is reflected in the line y = -2, what are the coordinates of e?

Explanation:

Step1: Calculate the distance from point E's y - coordinate to the line of reflection

The y - coordinate of point E is $y_E=-5$, and the equation of the line of reflection is $y = - 2$. The distance $d$ is $|-2-(-5)|=3$.

Step2: Determine the y - coordinate of the reflected point

Since the point is reflected over the horizontal line $y=-2$, the x - coordinate of the point remains the same. The y - coordinate of the reflected point $E'$ is found by moving the same distance on the other side of the line $y = - 2$. So, $y_{E'}=-2 + 3=1$. The x - coordinate of E is $x_E=-7$, and for a reflection over a horizontal line, $x_{E'}=x_E=-7$.

Answer:

$(-7,1)$