Question

triangle abc is shown below.
which point is the coordinate of the image of a under the transformation \\(\

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

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

Explanation:

Step1: Determine the coordinates of point A

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

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

\).

Step2: Perform the matrix transformation

The transformation matrix is \(T=

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

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

$$
LATEXBLOCK2
$$

Answer:

\((4,2)\)