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′(−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)

Answer 1

To find the coordinates \( A' \) and \( B' \) after dilation of the line segment \( AB \) with a scale factor of 13, centered at the origin, you can apply the following formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

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

For point \( A(-6, 3) \):

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

For point \( B(-12, 9) \):

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

Based on these calculations, neither of the provided options in your question matches the calculated dilated coordinates \( A'(-78, 39) \) and \( B'(-156, 117) \). Could you please double-check your options?