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
(8, 16)
open paren 8 comma 16 close paren
(2,4)
open paren 2 comma 4 close paren
(−0.5, 1)
open paren negative 0 point 5 comma 1 close paren
(20,12)
Responses
(8, 16)
open paren 8 comma 16 close paren
(2,4)
open paren 2 comma 4 close paren
(−0.5, 1)
open paren negative 0 point 5 comma 1 close paren
(20,12)
Answers
GPT-4o mini
To find the location of \( L' \) after dilating point \( L \) by a scale factor of 4 with the center of dilation at point \( L \), we can use the following formula for dilation:
\[
L' = L + k(L - L)
\]
where \( L \) is the original point, \( k \) is the scale factor, and \( L' \) is the dilated point.
Since \( L \) is at point \( (2, 4) \), the calculation simplifies because the point \( L \) does not change location during dilation as it is the center of dilation.
Thus, regardless of the scale factor, the coordinates of \( L' \) remain the same as those of \( L \):
\[
L' = (2, 4)
\]
Therefore, \( L' \) is located at **(2, 4)**.
\[
L' = L + k(L - L)
\]
where \( L \) is the original point, \( k \) is the scale factor, and \( L' \) is the dilated point.
Since \( L \) is at point \( (2, 4) \), the calculation simplifies because the point \( L \) does not change location during dilation as it is the center of dilation.
Thus, regardless of the scale factor, the coordinates of \( L' \) remain the same as those of \( L \):
\[
L' = (2, 4)
\]
Therefore, \( L' \) is located at **(2, 4)**.