Question

a. rotate triangle abc 90° clockwise about the origin.

Explanation:

Step1: Find the coordinates of points

The coordinates of \(A(-5,3)\), \(B(-2,1)\), \(C(-5,1)\)

Step2: Apply the rotation formula

The formula for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, -x)\)
For point \(A(-5,3)\):
\(x=-5,y = 3\), after rotation \(A'(3,5)\)
For point \(B(-2,1)\):
\(x=-2,y = 1\), after rotation \(B'(1,2)\)
For point \(C(-5,1)\):
\(x=-5,y = 1\), after rotation \(C'(1,5)\)

Answer:

The coordinates of the rotated triangle are \(A'(3,5)\), \(B'(1,2)\), \(C'(1,5)\)