Question

1. rotate \\( \triangle a b c \\) \\( 90^{circ} \\) clockwise about the origin followed by a reflection across the \\( y \\)-axis.

rotation
\\( (\square, \square) \\)
\\( (\square, \square) \\)
\\( (\square, \square) \\)

reflection
\\( (\square, \square) \\)
\\( (\square, \square) \\)
\\( (\square, \square) \\)

Explanation:

Step1: Find coordinates of \(A\), \(B\), \(C\)

From the graph, \(A(-2,1)\), \(B(0,3)\), \(C(3,0)\)

Step2: Apply \(90^{\circ}\) clockwise rotation formula \((x,y)\to(y, -x)\)

For \(A(-2,1)\): \((1,2)\)
For \(B(0,3)\): \((3,0)\)
For \(C(3,0)\): \((0,-3)\)

Step3: Apply reflection across \(y -\)axis formula \((x,y)\to(-x,y)\)

For \((1,2)\): \((-1,2)\)
For \((3,0)\): \((-3,0)\)
For \((0,-3)\): \((0,-3)\)

Answer:

Rotation: \((1,2)\), \((3,0)\), \((0, - 3)\)
Reflection: \((-1,2)\), \((-3,0)\), \((0,-3)\)