Dilations Centered at the Origin

If a line segment has endpoints at (2, 2) and (-2, -2) and undergoes a dilation with a scale factor of 2 centered at the origin, what are the coordinates of the new endpoints?

• (4, 4) and (-4, -4)

• (1, 1) and (-1, -1)

• (0, 0) and (0, 0)

• (2, 2) and (-2, -2)

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)

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)

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

Which of the following statements is true about dilations centered at the origin?

• They always result in a larger figure.

• They can only reduce the size of a figure.

• They preserve the shape of the figure.

• They change the shape of the figure.

What is the scale factor of a dilation that doubles the distance of every point from the origin?

• 0.5

• 1

• 2

• -2

• The figure's area becomes four times larger.

• The figure's area becomes twice as large.

• The figure's area is reduced to one-fourth.

• The figure's area is reduced to one-half.

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

• 3

• -3