The point (5, -7) is dilated by a scale factor of 4 about the origin. Find the location of the new point. Show your work.

Answer 1

New point: (20, -28). Slope of line going through the origin and (5, -7) is -7/5, which makes the radius of that circle sq rt of 74, or
(74)^(1/2). The new radius will be
4*(74)^(1/2). Assuming that the length of the x coordinate (and Y!) is proportional to the radius, that makes the new coordinate (20, -28). Double-checked it with the area of the circle, which increases by a factor of 16 (radius of original circle increased by a factor of 4: r of new circle = 16 times the r of old circle). Let me know if you agree!