Rectangle MATH is rotated 180 degrees about the origin. Use rotation mapping to solve for the coordinates of T'.

Question

Point M: (3, 4)
Point A: (5, 4)
Point T: (5, -1)
Point H: (3, -1)

Answer 1

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:

\[ T' = (-5, 1) \]