Question

The point A(5,-2) is reflected over the point (4, -5) and its image is point B. What are the coordinates of point B?

Answer 1

The position of a point or figure before any transformation is called "preimage"

After undergoing the transformation the resulting point/figure is called "preimage"

So for this exercise, the "preimage" is point A(5,-2)

This point was reflected over the point (4, -5)

To calculate the x-coordinate of B, first calculate the distance between the x-coordinates of point A and the reflection point.

$d_x=5-4=1$

Next subtract it to de x-coordinate of the reflection point

$x_B=4-1=3$

For the y-coordinate of B you have to follow the same method, first calculate the difference between the y-coordinates of point A and the reflection point:

$d_y=-2-(-5)=3$

Next subtract it from the y-coordinate of the reflecting point to determine the y-coordinate of B

$y_B=-5-3=-8$

The coordinates for point B are (3,-8)