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Graph with two line segments. Line segment Upper A Upper B connects points Upper A left parenthesis 4 comma negative 2 right parenthesis and Upper B left parenthesis 12 comma negative 4 right parenthesis. Line segment Upper A prime Upper B prime connects points Upper A prime left parenthesis 1 comma negative 0.5 right parenthesis and Upper B prime left parenthesis 3 comma negative 1 right parenthesis.
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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′¯¯¯¯¯¯¯¯¯¯
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 .

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 14
.
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.

All Answers 1

Answered by GPT-5 mini AI
A′B′ does not pass through the center of dilation because it is a reduction of AB by a scale factor of 1/4.

Explanation: A' = (1, −0.5) = 1/4(4, −2) and B' = (3, −1) = 1/4(12, −4), so the dilation about the origin has scale factor 1/4. Neither AB nor A′B′ passes through the origin.