What are the coordinates of vertex B’?

Question

Square ABCD is located on a coordinate plane. The coordinates for three of the vertices are listed: A (2,7), C (8,1), D (2,1) Square ABCD is dilated by a scale factor of 2 with the center of dilation at the origin, to form square A’ B’ C’ D’. What are the coordinates of vertex B’?

Answer 1

Plot the given points on a piece of graph paper. You should find three points that are the corners of a square. It's then pretty easy to see where the missing point would go. (This works even if you just sketch your own x and y axes with tick marks that are kinda equally spaced.) The missing corner B is at (8,7).

Since the center of dilation is at the origin, and it's dilated by a factor of two, each of the coordinates are moved to twice their original distance from the origin.

B(8,7) becomes B'(16,14).