Question

practice
reflect the figure over the line ( y = x ) to create quadrilateral ( chmw ). write the rule below and the coordinates next to each point ( (x,y)\to(y,x) )

1. quadrilateral ( chmw ) is shown on the coordinate grid.

reflect the figure over the line ( y=-x ) to create quadrilateral ( chmw ). write the rule below and the coordinates next to each point ( (x,y)\to(-y,-x) )

1. quadrilateral ( chmw ) is shown on the coordinate grid.

Explanation:

Left - hand side (Reflection over \(y = x\))

Step1: Find coordinates of \(C\), \(H\), \(M\), \(W\)

Assume \(C=(1,0)\), \(H=(4,2)\), \(M=(8, - 2)\), \(W=(0,-4)\)

Step2: Apply the rule \((x,y)\to(y,x)\)

For \(C=(1,0)\):
\(C'=(0,1)\)
For \(H=(4,2)\):
\(H'=(2,4)\)
For \(M=(8,-2)\):
\(M'=(-2,8)\)
For \(W=(0,-4)\):
\(W'=(-4,0)\)

Step1: Find coordinates of \(C\), \(H\), \(M\), \(W\)

Assume \(C=(1,0)\), \(H=(4,2)\), \(M=(8, - 2)\), \(W=(0,-4)\)

Step2: Apply the rule \((x,y)\to(-y,-x)\)

For \(C=(1,0)\):
\(C'=(0,-1)\)
For \(H=(4,2)\):
\(H'=(-2,-4)\)
For \(M=(8,-2)\):
\(M'=(2,-8)\)
For \(W=(0,-4)\):
\(W'=(4,0)\)

Answer:

\(C'=(0,1)\), \(H'=(2,4)\), \(M'=(-2,8)\), \(W'=(-4,0)\)

Right - hand side (Reflection over \(y=-x\))