Dilations of Lines

Given line m and point O not on line m. The image of line m is constructed through a dilation centered at O with a scale factor of 3. Which of the following statements best describes the image of line m?

• a line passing through point O

• a line intersecting with line m

• a line parallel to line m

• a line perpendicular to line m

Line AB is dilated with a center of dilation at A and a scale factor of 2. Which of the following statements will be true about and its image ?

• The slope of A'B' will be twice the slope of AB.

• The slope of A'B' will be half the slope of AB.

• The slope of A'B' will be two more than the slope of AB.

• The slope of A'B' will be the same as the slope of AB.

Point O is not on AB. When AB is dilated with the center of the dilation at O with a positive scale factor, A'B' is shorter than AB. What must be true about the scale factor?

• The scale factor is greater than 1.

• The scale factor is less than 1.

• The scale factor is 1.

• The lengths of AB and A'B' are not related to the scale factor.

If AB = 16 inches and AB is dilated by a scale factor of  $\frac{3}{2}$  , what is the length of A'B'? (Pay attention to units!)

• 16 inches

• 32 inches

• 2.5 feet

• 2 feet

The line represented by  $y=-\frac{1}{4}x-2$  is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

• The slope is  $-\frac{1}{4}$  and the y-intercept is -8.

• The slope is  $-\frac{1}{4}$  and the y-intercept is -2.

• The slope is -1 and the y-intercept is -8.

• The slope is -1 and the y-intercept is -2.

After a dilation with a center at (0, 0), the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is

•  $\frac{1}{5}$  

• 5

•  $\frac{1}{4}$  

• 4

The line $y=2x-4$  is dilated by a scale factor of  $\frac{3}{2}$  and centered at the origin.  Which equation represents the image of the line after the dilation?

• y = 2x - 4

• y = 2x - 6

• y = 3x - 4

• y = 3x - 6

The line y = -3x + 6 is dilated by a scale factor of 2 centered at the point (0, 6). Which equation represents the image of the line after the dilation?

• y = -3x + 12

• y = -3x + 6

• y = -6x + 12

• y = -6x + 6