Dilations Given Scale Factor and Center

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)

• (6,0), (9,-3), (-6,-15)

• (2/3,0), (1,-1/3), (-2/3,-5/3)

• (-1,-3), (0,-4), (-5,-8)

Which of the following are Dilations?

• (x, y) → (x, 3y)

• (x, y) → (3x, 3y)

• (x, y) → (x, y - 3)

• (x, y) → (.5x, .4y)

Does the image show a dilation?

• Yes

• No

What is the scale factor if the triangle on the left is the original?

• 2

• 3/2

• 2/3

• 1/2

In the figure above, a dilation from A to A' has occurred. What is the scale factor?

scale factor = _______

Mathematical Equivalence

ON

In the diagram below, CD is the image of AB after a dilation of scale factor k with center E. Which ratio is equal to the scale factor k of the dilation?

• EC : EA

• BA : EA

• EA : BA

• EA : EC

Match the following dilations by a scale factor of 1/2.

• (3,4)

• (6,8)

• (0, -5)

• (-6,-8)

• (-3, -4)

• (0,0)

• (5,1)

• (0, -10)

• (0,0)

• (10,2)

Answer explanation

Note that 0/2 is still 0

so (0,0) dilated by 1/2 is still at (0,0)

(0,-10) dilated by a 1/2 is at

(0, -5)

The table describes two dilations with the center of dilation at the origin. Which rule describes each dilation?

The table describes two dilations with the center of dilation at the origin. Which rule describes each dilation?

In the figure above, a dilation from A to A' has occurred. What is the scale factor?

Mathematical Equivalence

ON