Equation of a Dilated Line

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

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

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)

Tags

CCSS.8.G.A.3

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

Tags

CCSS.HSG.CO.A.2