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′(−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′(−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′(−6,3)
and B′(−4,3)
just choose one

Answer 1

To find the coordinates of the points A' and B' after dilation, we will apply the scale factor to the coordinates of points A and B.

The scale factor is 13, and the formulas for dilation centered at the origin are:
\[ A' = (kx, ky) \]
\[ B' = (kx, ky) \]
where \( (x,y) \) are the coordinates of point A or B, 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):
\[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]

Taking those calculations further with the response options provided:
1. A′(−18,9) and B′(−36,27) would be the correct scale as A = (−6,3) scales to (−18,9) and B = (−12,9) scales to (−36,27)

2. A′(−2,1) and B′(−4,3) is incorrect.

3. A′(−2,1) and B′(−12,9) is incorrect.

4. A′(−6,3) and B′(−4,3) is incorrect.

None of the choices given accurately reflect the dilation calculations as presented. If the calculation is actually directed based on the options stated at the beginning, I would suggest acknowledging that all given options might be incorrectly interpreted.

If based on the calculations being true to the dilation, the foresight remains specified out-of-tune with the exact values derived from dilating those points by factor of 13. Hence, choosing A′(−18,9) and B′(−36,27) fits a notice of accurate adjustments without miscalculation seen.

Therefore, the answer is:
**A′(−18,9) and B′(−36,27)**.