Question

graph △abc with vertices a(0,0), b(3,3), and c(4,0) and its image after a 90° rotation about the origin.

Explanation:

Step1: Apply the rotation rule

The rule for a \(90^{\circ}\) rotation about the origin \((x,y)\to(-y,x)\).
For point \(A(0,0)\):
Substitute \(x = 0\) and \(y=0\) into \((x,y)\to(-y,x)\)
\((0,0)\to(0,0)\)
For point \(B(3,3)\):
Substitute \(x = 3\) and \(y = 3\) into \((x,y)\to(-y,x)\)
\((3,3)\to(-3,3)\)
For point \(C(4,0)\):
Substitute \(x = 4\) and \(y=0\) into \((x,y)\to(-y,x)\)
\((4,0)\to(0,4)\)

Step2: Graph the original and rotated triangle

Plot the original points \(A(0,0)\), \(B(3,3)\), \(C(4,0)\) and the rotated points \(A'(0,0)\), \(B'(-3,3)\), \(C'(0,4)\) on the coordinate plane and connect the vertices for both \(\triangle ABC\) and \(\triangle A'B'C'\).

Answer:

The vertices of the image of \(\triangle ABC\) after a \(90^{\circ}\) rotation about the origin are \(A'(0,0)\), \(B'(-3,3)\), \(C'(0,4)\)