Question

triangle abc is shown below.

image of triangle abc on coordinate plane

which point is the coordinate of the image of a under the transformation \\( \

$$\begin{bmatrix} 0 & -1 \\\\ 1 & 0 \\end{bmatrix}$$

\\)?
\\( (-1, 2) \\)
\\( (-4, 2) \\)
\\( (-1, 7) \\)
\\( (2, -4) \\)

Explanation:

Step1: Determine the coordinates of point A

From the graph, the coordinates of point \(A\) are \((2,4)\). Represent \(A\) as a column vector \(

$$\begin{bmatrix}2\\4\end{bmatrix}$$

\).

Step2: Apply the transformation matrix

The transformation matrix is \(T=

$$\begin{bmatrix}0&-1\\1&0\end{bmatrix}$$

\). Multiply the matrix \(T\) by the column vector of \(A\):

$$
LATEXBLOCK2
$$

Answer:

\((-4,2)\)