Question

This image shows a rectangle on a coordinate plane, neatly defined by four labeled points: M, A, H, T. Here's a closer look:

Coordinates:

M is at (3, 4)

A is at (5, 4)

H is at (3, -1)

T is at (5, -1)

Details:

The axes extend from -6 to 6, offering a well-scaled grid for geometric exploration.

Orange lines connect the points to form the rectangle, and the blue labels add clarity.
Rectangle MATH
is rotated 180 degrees about the origin. Use rotation mapping to solve for the coordinates of T′
.

(1 point)
T′
(
,
)

Answer 1

To find the coordinates of point \( T' \) after rotating point \( T(5, -1) \) by 180 degrees about the origin, we can use the rotation mapping formula for a 180-degree rotation. The formula states:

\[
(x, y) \rightarrow (-x, -y)
\]

Applying this to the coordinates of point \( T \):

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

Thus, the coordinates of \( T' \) are:

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