Coordinate Geometry

Question

Copy the graph at the right. On the same set of axes, graph the image of MNOP for a dilation with center (0, 0) and scale factor 2. Use coordinate geometry and the definition of similar polygons to prove that MNOP is similar to its image.

For the graph just make a graph with points O(0,0) P(1,3) M(3,2) N(3,0)

Answer 1

What you need to do is graph the original four points. Since the center of dilation is (0,0) and a scale factor (enlargement) of 2 you multiply all of the coordinates by 2 to get M'N'O'P. Therefore,

M' = (6,4)

N' = (6,0)

O' = (0,0)

P' = (2,6)

Next you need to prove similarity. Recall the definition of similarity: same shape, proportional side lengths. You need to do a lot of distance formula equations to mathematically show you have the same ratio of

MN / M'N' = NO / N'O' = OP / O'P' = PM / P'M'