Question

Use the image to answer the question.

Line segment AB is translated to A prime B prime on a coordinate plane.

Image Long DescriptionThe graph displays two distinct line segments plotted on a coordinate plane. The x-axis ranges from 0 to 13, while the y-axis spans from negative 5 to 0. The first line segment, labeled Upper A Upper B, begins at point Upper A with coordinates left parenthesis 4 comma negative 2 right parenthesis and extends to point Upper B at left parenthesis 12 comma negative 4 right parenthesis. This segment slopes downward as it moves from left to right. The second line segment, labeled Upper A prime Upper B prime, starts at point Upper A prime with coordinates left parenthesis 1 comma negative 0.5 right parenthesis and ends at point Upper B prime at left parenthesis 3 comma negative 1 right parenthesis. This segment also slopes downward but is shorter and less steep compared to segment Upper A Upper B.

Determine whether the dilation passes through the center of dilation, if the center of dilation is the origin.

(1 point)
Responses

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
.
line segment upper a prime upper b prime does not pass through the center of dilation because it is taken to a line parallel to line segment upper A upper b .

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is a reduction of AB¯¯¯¯¯¯¯¯
by a scale factor of 1/4
.
line segment upper A prime upper b prime does not pass through the center of dilation because it is a reduction of line segment upper A upper b by a scale factor of 1 over 4 .

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is an enlargement of AB¯¯¯¯¯¯¯¯
by a scale factor of 4.
line segment upper A prime upper b prime passes through the center of dilation because it is an enlargement of line segment upper A upper b by a scale factor of 4.

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
.
line segment upper A prime upper B prime passes through the center of dilation because it is taken to a line parallel to line segment upper A upper B .

Answer 1

A′B′ does not pass through the center of dilation because A′ = (1,-0.5) = 1/4·(4,-2) and B′ = (3,-1) = 1/4·(12,-4), so it's a reduction of AB by scale factor 1/4 (the image is parallel to AB and does not include the origin).