Question

Graph triangle lmn with vertices l(1,6), m(-2,4), and n (3,2) and its

image after the composition.

Rotation: 90 about the origin

Translation: (x,y) (x-3,y+2)

Answer 1

To graph the triangle LMN with given vertices and apply rotation and translation to find its image.

Step-by-step explanation:

To graph the triangle LMN with vertices L(1,6), M(-2,4), and N(3,2), we plot these three points on a coordinate plane.

After that, we can apply the given transformations to find the image of the triangle. Firstly, we rotate the triangle 90 degrees about the origin by using the rotation matrix:

[x' y'] = [cos(θ) -sin(θ)][x y]

In this case, the rotation matrix becomes:

[x' y'] = [cos(90°) -sin(90°)][x y]

Simplifying this equation, we get:

[x' y'] = [-y x]

Next, we apply the translation by shifting each point (x, y) to (x-3, y+2). So, the image of each point becomes:

L': (1-3, 6+2) = (-2, 8)

M': (-2-3, 4+2) = (-5, 6)

N': (3-3, 2+2) = (0, 4)