Question

The vertices of a triangle are given in the columns of the matrix T= [0,4,0,0,0,5] If [-1,0,0,-1] is found to preform a transformation, what are the coordinates of the transformed triangle?​

Answer 1

A

Explanation:

E2020

Answer 2

(0,0), (-4,0), (0,-5).

Explanation:

Note: Matrices are not in proper format.

Consider the given matrix is

`T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}`

It means vertices are (0,0), (4,0) and (0,5).

Transformation matrix is

`A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}`

To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.

`AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}`

`AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}`

`AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}`

It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).