Question

Select the coordinates A′ 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′(−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) 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′(−12,9)

Answer 1

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

For point A(-6, 3):
- A' = (x * scale factor, y * scale factor)
- A' = (-6 * 13, 3 * 13)
- A' = (-78, 39)

For point B(-12, 9):
- B' = (x * scale factor, y * scale factor)
- B' = (-12 * 13, 9 * 13)
- B' = (-156, 117)

Thus, the new coordinates after the dilation will be:
- A' = (-78, 39)
- B' = (-156, 117)

None of the provided responses match. There has either been a misunderstanding or the options given are incorrect. Please check the scale factor or the original coordinates if you have any additional information.