Question

1. what is the outcome of translating △abc, where a(1, 1), b(3, 2), and c(3, 5) 5 units left and 1 unit up and then rotating it 180° ccw with a center of rotation at (-1, 2)? a(-4, 2), b(-2, 3), and c(-2, 6) a(2, 2), b(0, 1), and c(0, -2) a(0, -2), b(0, 1), and c(2, 2) a(0, -2), b(0, 1), and c(2, 2)

Explanation:

Step1: Translation

The translation rule for moving 5 units left and 1 unit up is \((x,y)\to(x - 5,y+1)\).
For point \(A(1,1)\): \(A'(1 - 5,1 + 1)=A'(-4,2)\)
For point \(B(3,2)\): \(B'(3 - 5,2 + 1)=B'(-2,3)\)
For point \(C(3,5)\): \(C'(3 - 5,5 + 1)=C'(-2,6)\)

Step2: Rotation

The rotation rule for a \(180^{\circ}\) counter - clockwise rotation about the point \((-1,2)\) is \((x,y)\to(-2 - x,4 - y)\)
For point \(A'(-4,2)\): \(A''(-2-(-4),4 - 2)=A''(2,2)\)
For point \(B'(-2,3)\): \(B''(-2-(-2),4 - 3)=B''(0,1)\)
For point \(C'(-2,6)\): \(C''(-2-(-2),4 - 6)=C''(0,-2)\)

Answer:

A("2, 2), B("0, 1), and C("0, -2)