Question

The vertices of a square are located at (2, 2), (5, 2), (5, 5), and (2, 5). The square is dilated by a scale factor of 2. The center of dilation is the origin (0, 0). What are the coordinates of the vertices of the image of the square?

A:(4, 4), (10, 4), (10, 10), (4, 10)
B:(1, 1), (2.5, 1), (1, 2.5), (2.5, 2.5)
C:(4, 4), (7, 4), (4, 7), (7, 7)D:(1, 1), (5, 1), (5, 1), (5, 5)

Answer 1

The coordinates of the image of the square after dilation with a scale factor of 2 and a center of dilation at the origin (0, 0) are (4, 4), (10, 4), (10, 10), and (4, 10).

Step-by-step explanation:

To find the coordinates of the image of the square after dilation, we need to multiply the coordinates of each vertex by the scale factor. Since the scale factor is 2, we will double the x-coordinate and the y-coordinate of each vertex. Here are the coordinates of the original square: (2, 2), (5, 2), (5, 5), and (2, 5). Doubling these coordinates gives us: (4, 4), (10, 4), (10, 10), and (4, 10). Therefore, the coordinates of the image of the square after dilation are (4, 4), (10, 4), (10, 10), and (4, 10).