Given a point (-6,4) in a line segment, what is the new point when the line segment is rotated counterclockwise about the origin 180 degrees

Answer 1

To rotate a point counterclockwise about the origin by 180 degrees, we can multiply the coordinates of the point by the matrix:

\[\begin{bmatrix}
-1 & 0 \\
0 & -1
\end{bmatrix}\]

When we apply this transformation to the point (-6,4), we get:

\[\begin{bmatrix}
-1 & 0 \\
0 & -1
\end{bmatrix} \begin{bmatrix}
-6 \\
4
\end{bmatrix} = \begin{bmatrix}
-1(-6) + 0(4) \\
0(-6) + (-1)(4)
\end{bmatrix} = \begin{bmatrix}
6 \\
-4
\end{bmatrix}\]

Therefore, the new point after rotating (-6,4) counterclockwise about the origin by 180 degrees is (6,-4).