Question
AB is dilated by a scale factor of 4, with a center of dilation at A. If A is at point (2,4) and B is at point (5,3), where would A' be located?
a. (20,12)
b. (2,4)
c. (8,16)
d. (-0.5,1)
a. (20,12)
b. (2,4)
c. (8,16)
d. (-0.5,1)
Answers
Answered by
GPT-4o mini
To find the location of the point A' after dilation, we need to use the formula for dilation. When dilating a point \( P(x, y) \) from a center of dilation \( O(a, b) \) by a scale factor of \( k \), the new point \( P' \) is given by:
\[
P' = O + k \cdot (P - O)
\]
where \( O \) is the center of dilation, \( P \) is the point being dilated, and \( P' \) is the resulting point after dilation.
In this case:
- The center of dilation \( A \) is at point \( (2,4) \).
- The point \( B \) is at point \( (5,3) \).
- The scale factor is \( 4 \).
Since we are dilating point \( A \), we simply need to understand that when a point is dilated from itself, the resulting point remains in the same location. Therefore:
\[
A' = A = (2,4)
\]
Thus, the coordinates of point A' after dilation are:
**b. (2,4)**
\[
P' = O + k \cdot (P - O)
\]
where \( O \) is the center of dilation, \( P \) is the point being dilated, and \( P' \) is the resulting point after dilation.
In this case:
- The center of dilation \( A \) is at point \( (2,4) \).
- The point \( B \) is at point \( (5,3) \).
- The scale factor is \( 4 \).
Since we are dilating point \( A \), we simply need to understand that when a point is dilated from itself, the resulting point remains in the same location. Therefore:
\[
A' = A = (2,4)
\]
Thus, the coordinates of point A' after dilation are:
**b. (2,4)**
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