Question
LM¯¯¯¯¯¯¯¯¯ is dilated by a scale factor of 4, with a center of dilation at L. If L is at point (2,4) and M is at point (5,3) , where would L′ be located?(1 point) Responses (2,4) open paren 2 comma 4 close paren (20,12) open paren 20 comma 12 close paren (−0.5, 1)
Answers
GPT-4o mini
To find the coordinates of the point \( L' \) after dilation, we start from the coordinates of point \( L \), which is \( (2, 4) \). The dilation is centered at point \( L \) and has a scale factor of 4.
The formula for the dilation of a point \( (x, y) \) from a center of dilation \( (x_c, y_c) \) by a scale factor \( k \) is given by:
\[
(x', y') = (x_c + k(x - x_c), y_c + k(y - y_c))
\]
In this case:
- \( L = (x_c, y_c) = (2, 4) \)
- \( k = 4 \)
- The coordinates to dilate are those of point \( L \) itself, which remain \( (2, 4) \).
Substituting into the formula:
\[
L' = (2 + 4(2 - 2), 4 + 4(4 - 4))
\]
Calculating each part:
- \( L' = (2 + 4(0), 4 + 4(0)) = (2, 4) \)
Thus, the coordinates of \( L' \) after dilation will remain \( (2, 4) \).
So the correct answer is: \( (2, 4) \).
The formula for the dilation of a point \( (x, y) \) from a center of dilation \( (x_c, y_c) \) by a scale factor \( k \) is given by:
\[
(x', y') = (x_c + k(x - x_c), y_c + k(y - y_c))
\]
In this case:
- \( L = (x_c, y_c) = (2, 4) \)
- \( k = 4 \)
- The coordinates to dilate are those of point \( L \) itself, which remain \( (2, 4) \).
Substituting into the formula:
\[
L' = (2 + 4(2 - 2), 4 + 4(4 - 4))
\]
Calculating each part:
- \( L' = (2 + 4(0), 4 + 4(0)) = (2, 4) \)
Thus, the coordinates of \( L' \) after dilation will remain \( (2, 4) \).
So the correct answer is: \( (2, 4) \).