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

Answer:

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Step-by-step explanation:

Answer 2

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

Step-by-step 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)