Question

A square on the coordinate plane has vertices at (−2, 2), (2, 2), (2, −2), and (−2, −2). A dilation of the square has vertices at (−6, 6), (6, 6), (6, −6), and (−6, −6). Find the scale factor and the perimeter of each square.

Answer 1

The scale factor between the squares is 2 and the perimeters are 16 units and 32 units respectively.

Step-by-step explanation:

The scale factor between the smaller square and the larger square is 2, meaning the dimensions of the larger square are twice that of the smaller square. The side length of the larger square is 8 units (4 units x 2). To find the perimeter of each square, we add up the lengths of all four sides. The perimeter of the smaller square is 4 + 4 + 4 + 4 = 16 units. The perimeter of the larger square is 8 + 8 + 8 + 8 = 32 units.