Let's start by plotting the given vertices L(- 4,- 3), M(- 1,- 1), and N(2,- 2). Then we will connect them with line segments to draw the triangle.
We will now draw the image of LMN after a 180^(∘) clockwise rotation about vertex M. For simplicity, let's start by rotating only one point. We will use vertex N. To do so, we will use a protractor to draw a ray that makes a 180^(∘) angle with MN at M. Remember that a rotation by 180^(∘) ends up in the same place no matter which direction we go.
On this ray, we will mark a point N' that is the same length as MN. This is the image of N after the rotation.
Next, we will repeat the same process for vertex L to find L'. Since M is the point at which the triangle is rotated, M' will be in the same position as M. The coordinates of the images of the vertices are L'(2,1), M'(- 1, - 1), and N'(- 4,0).
Finally, we will connect L', M', and N' to obtain the image of LMN.
Extra
Visualizing the Rotation
Let's rotate △ LMN 180^(∘) clockwise about M so that we can see how it is mapped onto △ L'M'N'.
