Understanding Dilations Centered at the Origin

What is the scale factor of a dilation that reduces a shape to one-third of its original size?

• 3

• -3

If the point (4, -6) is dilated with a scale factor of 2 centered at the origin, what are the coordinates of the image?

• (2, -3)

• (8, -12)

• (-8, 12)

• (4, -6)

Which of the following scale factors would result in an enlargement of the original figure?

• 1

• 2

• -1

• (12, 20)

• (0.75, 1.25)

• (-3, -5)

• (3, 5)

What is the effect of a dilation with a scale factor of 1 centered at the origin?

• The figure is enlarged.

• The figure is reduced.

• The figure remains unchanged.

• The figure is reflected.

A triangle has vertices at (2, 3), (4, 5), and (6, 7). If the triangle is dilated with a scale factor of 0.5 centered at the origin, what are the coordinates of the new vertices?

• (1, 1.5), (2, 2.5), (3, 3.5)

• (1, 1.5), (2, 2.5), (4, 3.5)

• (4, 6), (8, 10), (12, 14)

• (1, 1.5), (2, 2.5), (3, 3.5)

What happens to the orientation of a figure after a dilation centered at the origin?

• It flips over the x-axis.

• It flips over the y-axis.

• It remains the same.

• It rotates 180 degrees.

If a square has side lengths of 4 units and undergoes a dilation with a scale factor of 3 centered at the origin, what will be the length of each side of the resulting square?

• 12 units

• 7 units

• 4 units

• 1.33 units

A dilation centered at the origin with a scale factor of -2 will result in which of the following?

• An enlargement and a reflection across the origin

• A reduction and a reflection across the origin

• An enlargement without reflection

• A reduction without reflection

If the coordinates of a point after dilation are (-6, 9) and the scale factor was 3, what were the original coordinates of the point?

• (-2, 3)

• (2, -3)

• (-18, 27)

• (18, -27)