Question

Use matrices to determine the coordinates of the vertices of the rotated figure. Rot 90 for triangleMNP with vertices M(-2,6), N(7,1), and P(4,-3)​

Answer 1

this is the answer. thank me later!

Explanation:

Answer 2

Coordinate of image triangle is M'(-6,-2),N'(-1,7) and P'(3,4)

Explanation:

The given triangle MNP has coordinates of M(-2,6), N(7,1), and P(4,-3)​

In matrix form, It can be written as :

`\left[\begin{array}{ccc}-2&7&4\\6&1&-3\\\end{array}\right]`

Triangle has to rotate by angle of 90 degree at origin.

Counterclockwise Rotation matrix is given by :

`\left[\begin{array}{ccc}cos\theta&-sin\theta\\sin\theta&cos\theta\end{array}\right]`

For
`\theta = 90`

`\left[\begin{array}{ccc}0&-1&\\1&0\end{array}\right]`

Image of triangle MNP will be

=
`\left[\begin{array}{ccc}0&-1&\\1&0\end{array}\right]`
`\left[\begin{array}{ccc}-2&7&4\\6&1&-3\\\end{array}\right]`

=
`\left[\begin{array}{ccc}-6&-1&3\\-2&7&4\\\end{array}\right]`

Thus,

The coordinate of image triangle is M(-6,-2),N(-1,7) and P(3,4)