Dilation Dynamics: Scaling the Coordinate Plane

If the point (3, -4) is dilated with a scale factor of 2 centered at the origin, what will be the coordinates of the image?

• (1.5, -2)

• (6, -8)

• (3, -4)

• (0, 0)

A triangle has vertices at (1, 1), (4, 1), and (1, 3). If the triangle is dilated by a scale factor of 3 with the center of dilation at the origin, what are the coordinates of the image's vertices?

• (3, 3), (12, 3), (3, 9)

• (3, 3), (7, 3), (3, 6)

• (1, 1), (4, 1), (1, 3)

• (2, 2), (8, 2), (2, 6)

What is the effect of a scale factor of 1/2 on the coordinates of a point (x, y) when dilated with respect to the origin?

• The image will be twice as far from the origin.

• The image will be at the same location as the original point.

• The image will be half as far from the origin.

• The image will be at the origin.

Given a rectangle with vertices at (2, 2), (2, -2), (-2, -2), and (-2, 2), after a dilation with a scale factor of 0.5 centered at the origin, what will be the coordinates of the new vertices?

• (1, 1), (1, -1), (-1, -1), (-1, 1)

• (4, 4), (4, -4), (-4, -4), (-4, 4)

• (2, 2), (2, -2), (-2, -2), (-2, 2)

• (0.5, 0.5), (0.5, -0.5), (-0.5, -0.5), (-0.5, 0.5)

If a line segment has endpoints at (-3, 6) and (3, -6) and is dilated by a scale factor of 3 with the center of dilation at the origin, what will be the length of the dilated line segment compared to the original?

• The length will be the same.

• The length will be three times longer.

• The length will be one-third of the original.

• The length will be nine times longer.