Part
In a new quilt design, Sonja is using triangles. She
does not want the quilt to be centered, to give it
more visual interest. Therefore, Sonja plans to
rotate the triangle design 90° over and over
about the point (5, -1).
10
9
8
7
5
4
3
1 2 3 4 5
Explain how Sonja would determine the location
of the next triangle in the design.
-5
6
-7
-8
-9
-

For Sonja to determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by [tex]90^o[/tex].

From the question, we have:

[tex]C = (5,-1)[/tex] --- the center of rotation

Let the vertices of the triangle be (x,y).

First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.

This gives:

[tex](x,y) \to (x - 5, y + 1)[/tex]

Then the vertices are rotated by [tex]90^o[/tex]

The rule of [tex]90^o[/tex] rotation is:

[tex](x,y) \to (-y,x)[/tex]

So, we have:

[tex](x - 5,y + 1) \to (-y - 1,x - 5)[/tex]

From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)

After rotation, the coordinates are calculated as follows:

[tex](0,2) \to (-2-1,0-5) \to (-3,-5)[/tex]

[tex](0,5) \to (-5-1,0-5) \to (-6,-5)[/tex]

[tex](4,2) \to (-2-1,4-5) \to (-3,-1)[/tex]

Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)