Question

A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is rotated 90° clockwise around the origin?

Answer 1

for 90 clockwise it is (x,y) -> (y, -x)

Answer 2

$$
A~rotation~by ~90^\circ means:\\\\
\begin{bmatrix}
A_x &A_y \\
B_x &B_y \\
C_x &C_y
\end{bmatrix}
\begin{bmatrix}
0 &-1 \\
1 &\quad \!\! 0
\end{bmatrix}
=
\begin{bmatrix}
A_y &-A_x \\
B_y &-B_x \\
C_y &-C_x
\end{bmatrix}
\\\\
\text{Therefore,}
\\\\
\begin{bmatrix}
\quad 1 &\quad 5 \\
-2 & \quad 1 \\
\quad 0 & -4
\end{bmatrix}
\begin{bmatrix}
0 &-1 \\
1 &\quad \!\!0
\end{bmatrix}
=
\begin{bmatrix}
\quad 5 &-1 \\
\quad 1 &\!\!\quad 2 \\
-4 & \!\!\quad 0
\end{bmatrix}
\\\\
Rotated~vectors~are~\vec{A}=<5,-1>\vec{B}=<1,2>\vec{C}=<-4,0>
$$