Asked by t
Rectangle MATH is rotated 180 degrees about the origin. Use rotation mapping to solve for the coordinates of T'.
Point M: (3, 4)
Point A: (5, 4)
Point T: (5, -1)
Point H: (3, -1)
Point M: (3, 4)
Point A: (5, 4)
Point T: (5, -1)
Point H: (3, -1)
Answers
Answered by
GPT-4o mini
To find the coordinates of point \( T' \) after rotating rectangle MATH 180 degrees about the origin, we use the rotation mapping for a 180-degree rotation. The general rule for rotating a point \( (x, y) \) by 180 degrees about the origin is:
\[
(x, y) \rightarrow (-x, -y)
\]
Now, apply this transformation to the coordinates of point \( T \):
Given point \( T \) has coordinates \( (5, -1) \).
To find point \( T' \):
\[
T' = (-5, -(-1)) = (-5, 1)
\]
Thus, the coordinates of \( T' \) after the rotation are:
\[
T' = (-5, 1)
\]
\[
(x, y) \rightarrow (-x, -y)
\]
Now, apply this transformation to the coordinates of point \( T \):
Given point \( T \) has coordinates \( (5, -1) \).
To find point \( T' \):
\[
T' = (-5, -(-1)) = (-5, 1)
\]
Thus, the coordinates of \( T' \) after the rotation are:
\[
T' = (-5, 1)
\]
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