Dilations Through the Origin

The line whose equation is 3x – 5y = 4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?

• The image of the line has the same slope as the pre-image but a different y-intercept.

• The image of the line has the same y-intercept as the pre-image but a different slope.

• The image of the line has the same slope and the same y-intercept

  as the pre-image.

• The image of the line has a different slope and a different y-intercept from the pre-image.

The line 3y = -2x + 8 is transformed by a dilation centered at the origin. Which linear equation could be its image?

• 2x + 3y = 5

• 2x - 3y = 5

• 3x + 2y = 5

• 3x - 2y = 5

Line segment A'B' whose endpoints are (4, -2) and (16, 14) is the image of AB after a dilation of 1/2 centered at the origin. What is the length of AB?

• 5

• 10

• 20

• 40

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

• 1/5

• 5

• 1/4

• 4

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)

Is the following a dilation?

• Yes

• No

The line represented by the equation 4y = 3x+7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

• 3x - 4y = 9

• 3x + 4y = 9

• 4x - 3y = 9

• 4x + 3y = 9

A line that passes through the points whose coordinates are (1,1) and (5, 7) is dilated by a scale factor of 3 and centered at the origin. The image of the line

• is perpendicular to the original line

• is parallel to the original line

• passes through the origin

• is the original line

Determine which point (A, B, C, or D) represents the center of dilation.

• A

• B

• C

• D

Dilate the given preimage by a scale factor of 4 with a center at the origin.  Draw the dilation on the grid.