Dilation Around the Origin

Triangle ABC is dilated using a scale factor of 1/2. The center of dilation is at the origin. What are the new coordinates of point A'?

• (-3, 3)

• (-12, 12)

• (-2, 2)

Triangle EFG is drawn on the coordinate plane. The triangle is dilated by a scale factor of 1/3, with the center of dilation at the origin, to form triangle E'F'G'. Then, triangle E'F'G' is translated 3 units to the right to form triangle E''F''G''. What is the coordinate of E'' ?

When the scale factor of a dilation is between 0 and 1, the dilation is a reduction (shrinks).

• True

• False

Point B (-10,-6) is dilated with a scale factor of 1/2 and the center of dilation at the origin. What are the coordinated of B'?

• (5,3)

• (20,12)

• (-20,-12)

• (-5,-3)

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

• F

• G

• H

• J

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.

The scale factor for this dilation is:

Mathematical Equivalence

ON

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.