Select the coordinates A′

Question

and B′
after dilation of the line segment AB
with a scale factor of 13
, centered at the origin where the endpoints are A(−6,3)
and B(−12,9)
.(1 point)
Responses

A′(−6,3)
and B′(−4,3)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−2,1)
and B′(−4,3)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−18,9)
and B′(−36,27)
upper A prime left parenthesis negative 18 comma 9 right parenthesis and upper B prime left parenthesis negative 36 comma 27 right parenthesis

A′(−2,1)
and B′(−12,9)

Answer 1

To find the coordinates of points A' and B' after dilation with a scale factor of 13, centered at the origin, we multiply the coordinates of points A and B by the scale factor.

For point \( A(-6, 3) \): \[ A' = \left(-6 \times 13, 3 \times 13\right) = (-78, 39) \]

For point \( B(-12, 9) \): \[ B' = \left(-12 \times 13, 9 \times 13\right) = (-156, 117) \]

Thus, the coordinates after dilation are: \[ A'(-78, 39) \text{ and } B'(-156, 117) \]

None of the given responses match these coordinates, suggesting a mistake may have been made in the options provided. Please check the options or specify the scale factor and points if this information is incorrect.