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′(−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′(−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′(−6,3) and B′(−4,3)

Answer 1

To find the coordinates \( A' \) and \( B' \) after applying a dilation with a scale factor of 13 centered at the origin, we will use the formula for dilation:

\[ A' = (kx, ky) \]

where \( (x, y) \) are the coordinates of the original point and \( k \) is the scale factor.

Given:

• \( A(-6, 3) \)
• \( B(-12, 9) \)
• Scale factor \( k = 13 \)

For Point A:

\[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]

For Point B:

\[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]

Thus, the coordinates after dilation are:

• \( A'(-78, 39) \)
• \( B'(-156, 117) \)

None of the provided responses match these results. If you require further assistance, please provide additional context or verify the options provided.