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′(−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)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 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′(−6,3)
and B′(−4,3)

Answer 1

To find the coordinates \( A' \) and \( B' \) after dilation of the points \( A(-6, 3) \) and \( B(-12, 9) \) with a scale factor of 13, centered at the origin, we need to multiply each coordinate of the points by the scale factor.

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

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

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

It appears that neither of these coordinates matches any of the responses you provided. Please check the scale factor or the initial coordinates for accuracy.