Question
Find the dilation of 0.25 with the center (0, 0) for the following points:A (0,−4)B (0, 2)(2 points)A′ =B′ =
Answers
Answer
b is not right
Answered by
GPT-4o mini
To find the dilation of a point with respect to a center and a scale factor, you can use the formula:
\[
A' = (kx, ky)
\]
where \( A'(x', y') \) is the new point after dilation, \( (x, y) \) is the original point, \( k \) is the scale factor, and \( (0, 0) \) is the center of dilation.
Given a scale factor \( k = 0.25 \), we can find the dilations for points \( A(0, -4) \) and \( B(0, 2) \):
1. For point \( A(0, -4) \):
\[
A' = (0.25 \cdot 0, 0.25 \cdot -4) = (0, -1)
\]
2. For point \( B(0, 2) \):
\[
B' = (0.25 \cdot 0, 0.25 \cdot 2) = (0, 0.5)
\]
Thus, the points after dilation are:
\( A' = (0, -1) \) and \( B' = (0, 0.5) \).
\[
A' = (kx, ky)
\]
where \( A'(x', y') \) is the new point after dilation, \( (x, y) \) is the original point, \( k \) is the scale factor, and \( (0, 0) \) is the center of dilation.
Given a scale factor \( k = 0.25 \), we can find the dilations for points \( A(0, -4) \) and \( B(0, 2) \):
1. For point \( A(0, -4) \):
\[
A' = (0.25 \cdot 0, 0.25 \cdot -4) = (0, -1)
\]
2. For point \( B(0, 2) \):
\[
B' = (0.25 \cdot 0, 0.25 \cdot 2) = (0, 0.5)
\]
Thus, the points after dilation are:
\( A' = (0, -1) \) and \( B' = (0, 0.5) \).
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