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′(−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′(−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′(−2,1)
and B′(−12,9)

Answer 1

To find the coordinates of the points \( A' \) and \( B' \) after dilation with a scale factor of 13 centered at the origin, we will multiply the coordinates of points \( A \) and \( B \) by the scale factor.

Given:
- \( A(-6, 3) \)
- \( B(-12, 9) \)
- Scale factor = 13

**Step 1: Dilation of Point A**
\[
A' = (k \cdot x, k \cdot y) = (13 \cdot -6, 13 \cdot 3) = (-78, 39)
\]

**Step 2: Dilation of Point B**
\[
B' = (k \cdot x, k \cdot y) = (13 \cdot -12, 13 \cdot 9) = (-156, 117)
\]

So the coordinates after dilation are:
- \( A'(-78, 39) \)
- \( B'(-156, 117) \)

Looking at the provided options, none of them correspond to the calculated coordinates. If we strictly follow the calculation steps and the defined scale factor, the correct results based on dilation calculations do not match the provided choices. Please double-check the original problem statements, or if any scale factor or coordinates were misstated.

If your intention is to find a different scale or transform, please provide that clarification. Alternatively, if this was meant to be a smaller scale factor adjustment, the process would be similar, and we could adjust those values accordingly.