Question

A line with the equation y=13x−7 is dilated with a scale factor of 3 and a center at (x, -9). The line maps onto itself after the dilation. The y-coordinate of the center of the dilation is − 9. What is the x-coordinate of the dilation?

Answer 1

In order for the dilated line to map to itself, the center of dilation must be a point on the line. The x-coordinate can be found from
-9 = 13x -7
-2 = 13x
-2/13 = x

The x-coordinate of the center of dilation is -2/13.