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′(−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′(−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′(−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)

1 answer

To find the coordinates of the points A' and B' after dilation with a scale factor of 13 centered at the origin, you can use the formula for dilation:

\[ (x, y) \to (kx, ky) \]

where \(k\) is the scale factor. For this problem, \(k = 13\).

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

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

Neither of these coordinates match the options provided in your responses. However, it appears you might have a mix-up in the understanding of the scale factor—if you were indeed referring to a different scale, please clarify.

Nonetheless, based on the scale factor of 13 as per your request, the correct coordinates A' and B' would be:

A'(-78, 39) and B'(-156, 117).

Double-check the scale factor and your expected outcomes against the response options, or kindly clarify if there’s been an error or misunderstanding in input.