Question

1. what is the outcome of reflecting △abc, where a(1,1), b(3,2), and c(3,5) over the y - axis and then rotating it 180° ccw? a(\1,1), b(\3,2), and c(\3,5) a(\1, - 1), b(\3, - 2), and c(\3, - 5) a(\1, - 1), b(-3,2), and c(3, - 5) a(-1, - 1), b(\-3, - 2), and c(\-3, - 5)

Explanation:

Step1: Reflection over the y - axis

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\).
For point \(A(1,1)\), after reflection over the y - axis, \(A'( - 1,1)\).
For point \(B(3,2)\), after reflection over the y - axis, \(B'(-3,2)\).
For point \(C(3,5)\), after reflection over the y - axis, \(C'(-3,5)\).

Step2: Rotation of \(180^{\circ}\) counter - clockwise

The rule for a \(180^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-x,-y)\).
For point \(A'(-1,1)\), after rotation, \(A''(1,-1)\).
For point \(B'(-3,2)\), after rotation, \(B''(3,-2)\).
For point \(C'(-3,5)\), after rotation, \(C''(3,-5)\).

Answer:

A(1, - 1), B(3, - 2), and C(3, - 5) (corresponding to the first option \(A''(1,-1),B''(3,-2),\text{and }C''(3,-5)\))