Question

Trangle LMN has the vertices L(2,-2), M(7,-3), and N(5,2). Find the coordinates of the vertices after a 270 degree rotation about point M

Answer 1

To find the coordinates of the vertices after a 270 degree rotation about point M, you can use the rotation formula. The new coordinates for vertex L after the rotation are (-5, 3), for vertex M are (0, 0), and for vertex N are (-4, 2).

Step-by-step explanation:

To find the coordinates of the vertices after a 270 degree rotation about point M, we can use the rotation formula. The rotation formula for a point (x, y) about point (a, b) by an angle theta is:

x' = (x-a)cos(theta) - (y-b)sin(theta)

y' = (x-a)sin(theta) + (y-b)cos(theta)

So, using this formula, we can calculate the new coordinates for each vertex. For vertex L(2, -2):

x' = (2-7)cos(270) - (-2-(-3))sin(270) = -5

y' = (2-7)sin(270) + (-2-(-3))cos(270) = 3

Hence, the new coordinates for vertex L after the rotation are (-5, 3). Similarly, you can find the new coordinates for vertices M and N.

For vertex M(7, -3), the new coordinates will be:

x' = (7-7)cos(270) - (-3-(-3))sin(270) = 0

y' = (7-7)sin(270) + (-3-(-3))cos(270) = 0

So, the new coordinates for vertex M after the rotation are (0, 0).

For vertex N(5, 2), the new coordinates will be:

x' = (5-7)cos(270) - (2-(-3))sin(270) = -4

y' = (5-7)sin(270) + (2-(-3))cos(270) = 2

Therefore, the new coordinates for vertex N after the rotation are (-4, 2).