Question

Draw ALMN with vertices L(3,-1), M(7,-3), and N(6,3). Find the coordinates of the vertices after a 90° rotation about the origin and about each of the points L, M, and N. what are the coordinates of the points after a 90° rotation about the origin? L=? M=? N=?

Answer 1

The coordinates of the points after a 90° rotation about the origin are: L(1,3), M(3,7), and N(-3,6).

Step-by-step explanation:

To find the coordinates of the points after a 90° rotation about the origin, we will use the following formula:

(x', y') = (x cos θ - y sin θ, x sin θ + y cos θ)

Given the original coordinates: L(3,-1), M(7,-3), and N(6,3), we can calculate the new coordinates as follows:

For point L:
x' = 3 cos 90° - (-1) sin 90° = 0 - (-1) = 1
y' = 3 sin 90° + (-1) cos 90° = 3 + 0 = 3
So, the new coordinates for point L after a 90° rotation about the origin are (1,3).

For point M:
x' = 7 cos 90° - (-3) sin 90° = 0 - (-3) = 3
y' = 7 sin 90° + (-3) cos 90° = 7 + 0 = 7
So, the new coordinates for point M after a 90° rotation about the origin are (3,7).

For point N:
x' = 6 cos 90° - 3 sin 90° = 0 - 3 = -3
y' = 6 sin 90° + 3 cos 90° = 6 + 0 = 6
So, the new coordinates for point N after a 90° rotation about the origin are (-3,6).