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) . 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, we use the formula for dilation centered at the origin:

\[
A' = k \cdot A
\]

\[
B' = k \cdot B
\]

where \( k \) is the scale factor and \( A \) and \( B \) are the original coordinates of the endpoints.

In this case, the scale factor \( k \) is 13, and the points are:

- \( A(-6, 3) \)
- \( B(-12, 9) \)

Now, we calculate the coordinates of the points after dilation.

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

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

So, the new coordinates of the points after dilation are:

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

From the provided options, none match the calculated values. Please check the options again or any specific details for incorrect input.