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 :

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

Counterclockwise Rotation matrix is given by :

For

Image of triangle MNP will be

=

=

Thus,

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

For Problem 10: side VS is approximately 7.07 but the exact number is 7.07106781187 which is the square root of 50. Side VS and ST are the same side length. VU and TU are also the same side length as each other, their length is 13. For 11:  side ST and VS is the square root of 145, which in exact form is 12.0415945788, and sie VU and UT is the square root of 130, which in exact form is 11.401754251

Step-by-step explanation:

In order to get sides ST and VS you have the side lengths 5 and 5 for each line, so the pythagorean theorem is a^2 + b^2 = c^2 so 5^2 + 5^2 is 25+25=50 You then get the square root of 50 to find C because 50 is C^2 and the square root of 50 is 7.07106781187. Use this for all the rest of the sides if you are still confused.