Dilating a Line Equations

A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

• The line segments are perpendicular, and the image is one-half of the length of the given line segment.

• The line segments are perpendicular, and the image is twice the length of the given line segment.

• The line segments are parallel, and the image is twice the length of the given line segment.

• The line segments are parallel, and the image is one-half of the length of the given line segment

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.

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

A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?

• 9 inches

• 2 inches

• 15 inches

• 18 inches

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

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

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

On the graph below, point A(3, 4) and BC with coordinates B(4, 3) and C(2, 1) are graphed. What are the coordinates of B' and C' after BC undergoes a dilation centered at point A with a scale factor of 2?

• B'(5,2) and C'(1, -2)

• B'(6, 1) and C'(0, -1)

• B'(5, 0) and C'(1, -2)

• B'(5, 2) and C'(3, 0)

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