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)​

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 : [tex]\left[\begin{array}{ccc}-2&7&4\\6&1&-3\\\end{array}\right][/tex]Triangle has to rotate by angle of 90 degree at origin.Counterclockwise Rotation matrix is given by :[tex]\left[\begin{array}{ccc}cos\theta&-sin\theta\\sin\theta&cos\theta\end{array}\right][/tex]For [tex]\theta = 90[/tex][tex]\left[\begin{array}{ccc}0&-1&\\1&0\end{array}\right][/tex]Image of triangle MNP will be =[tex]\left[\begin{array}{ccc}0&-1&\\1&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-2&7&4\\6&1&-3\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}-6&-1&3\\-2&7&4\\\end{array}\right][/tex]Thus,The coordinate of image triangle is M(-6,-2),N(-1,7) and P(3,4)