Dilations Centered at the Origin

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

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

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

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 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)

A dilation can produce a smaller figure or a(n)______

• reduction

• enlargement

• scale factor

• center of dilation

Which of the following are Dilations?

• (x, y) → (x, 3y)

• (x, y) → (3x, 3y)

• (x, y) → (x, y - 3)

• (x, y) → (.5x, .4y)

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

• 2

• 3/2

• 2/3

• 1/2

What is the scale factor if the smaller rectangle is the original rectangle?

• 4

• 25

• 5

• 6