Question

a figure is reflected over the lines y= -2 and y = -10. determine how far apart the preimage and image are.

Answer 1

We will have the following:

Since the figure is reflected over the lines y = -2 and y = -10 (Is relfected over the x-axis) we will have that the distance between the figue and it's pre-images will be:

*For the image over y = -2:

`d=2\sqrt[]{(-2-y)^2}\Rightarrow d=2|-y-2|`

*For the image over y = -10:

`d=2\sqrt[]{(-10-y)^2}\Rightarrow d=2|-y-10|`

The reason the y is in the answer for both is that the distance (or at leas the points of the figure) are not known, so y represents the distance between the figure and the reflection axis; and the reason it is multiplied by two is that the distance between the image and the pre-image is twice the distance between the figure and the reflection axis.