Question

Part

Answer 1

When a shape is rotated, it must be rotated around a point.

To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by $90^o$.

From the question, we have:

$C = (5,-1)$ --- 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:

$(x,y) \to (x - 5, y + 1)$

Then the vertices are rotated by $90^o$

The rule of $90^o$ rotation is:

$(x,y) \to (-y,x)$

So, we have:

$(x - 5,y + 1) \to (-y - 1,x - 5)$

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

After rotation, the coordinates are calculated as follows:

$(0,2) \to (-2-1,0-5) \to (-3,-5)$

$(0,5) \to (-5-1,0-5) \to (-6,-5)$

$(4,2) \to (-2-1,4-5) \to (-3,-1)$

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

Read more about rotations at:

brainly.com/question/1571997