Question

A coordinate plane's x-axis ranges from negative 2 to 8 and its y-axis ranges from negative 1 to 7, both by 1-unit increments. Point upper A, point upper B, and an unlabeled third point are plotted and connected by lines.
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The coordinates of points upper A and upper B are located as follows: upper A at left parenthesis 2 comma 4 right parenthesis and upper B at left parenthesis 6 comma 6 right parenthesis. The third unlabeled point is located at the origin. The line connecting point upper A with upper B is solid. The line connecting upper B with the origin point is a hybrid solid and dotted line that extends past the origin and past upper B. The line connecting upper A with the origin point is a dotted line that extends past the origin and past upper A.


A dilation of AB¯¯¯¯¯¯¯¯
occurs using a scale factor of 12
and a center of dilation at the origin. Prove that A′B′¯¯¯¯¯¯¯¯¯¯
is half the length of AB¯¯¯¯¯¯¯¯
by finding the points A′
and B′
.

(1 point)
Responses

A′
is at (4,8)
and B′
is at (12,12)
.
upper A prime is at left parenthesis 4 comma 8 right parenthesis and upper B prime is at left parenthesis 12 comma 12 right parenthesis .

A′
is at (−1,−2)
and B′
is at (−3,−3)
.
upper A prime is at left parenthesis negative 1 comma negative 2 right parenthesis and upper B prime is at left parenthesis negative 3 comma negative 3 right parenthesis .

A′
is at (1,5)
and B′
is at (3,6)
.
upper A prime is at left parenthesis 1 comma 5 right parenthesis and upper B prime is at left parenthesis 3 comma 6 right parenthesis .

A′
is at (1,2)
and B′
is at (3,3)
.

Answer 1

A dilation with center at the origin and scale factor 1/2 multiplies each coordinate by 1/2.

A = (2,4) -> A' = (2·1/2, 4·1/2) = (1,2)
B = (6,6) -> B' = (6·1/2, 6·1/2) = (3,3)

Thus A'B' is half the length of AB (lengths scale by the factor 1/2). The correct choice is A' = (1,2) and B' = (3,3).