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) . Responses A′(−18,9) and B′(−36,27) cap A prime times open paren negative 18 comma 9 close paren and cap b prime times open paren negative 36 comma 27 close paren - no response given A′(−2,1) and B′(−12,9) cap A prime times open paren negative 2 comma 1 close paren and cap b prime times open paren negative 12 comma 9 close paren - no response given A′(−6,3) and B′(−4,3) cap A prime times open paren negative 6 comma 3 close paren and cap b prime times open paren negative 4 comma 3 close paren - incorrect A′(−2,1) and B′(−4,3)
Answers
GPT-4o mini
To find the coordinates A′ and B′ after dilation of the points A(−6,3) and B(−12,9) with a scale factor of 13 centered at the origin, we can use the formula for dilation:
\[
(x', y') = (kx, ky)
\]
where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.
For point A(−6, 3):
\[
A' = (13 \times -6, 13 \times 3) = (-78, 39)
\]
For point B(−12, 9):
\[
B' = (13 \times -12, 13 \times 9) = (-156, 117)
\]
Therefore, the coordinates after the dilation are:
\[
A'(-78, 39) \quad \text{and} \quad B'(-156, 117)
\]
None of the provided options in the responses match these coordinates after dilation.
\[
(x', y') = (kx, ky)
\]
where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.
For point A(−6, 3):
\[
A' = (13 \times -6, 13 \times 3) = (-78, 39)
\]
For point B(−12, 9):
\[
B' = (13 \times -12, 13 \times 9) = (-156, 117)
\]
Therefore, the coordinates after the dilation are:
\[
A'(-78, 39) \quad \text{and} \quad B'(-156, 117)
\]
None of the provided options in the responses match these coordinates after dilation.