Question

1. translate trapezoid bear by the rule $(x,y)\to(x + 4,y - 2)$ followed by a reflection over the line $y=x$.

Explanation:

Step1: Find coordinates of trapezoid BEAR

Assume the coordinates of the vertices of trapezoid \(BEAR\) are \(B(-5,0)\), \(E(-1,4)\), \(A(0,4)\), \(R(0,0)\)

Step2: Translate using the rule \((x,y)\to(x + 4,y-2)\)

For point \(B(-5,0)\):
\(x=-5+4=-1\), \(y = 0-2=-2\), new coordinate \((-1,-2)\)
For point \(E(-1,4)\):
\(x=-1 + 4=3\), \(y=4-2 = 2\), new coordinate \((3,2)\)
For point \(A(0,4)\):
\(x=0+4 = 4\), \(y=4-2=2\), new coordinate \((4,2)\)
For point \(R(0,0)\):
\(x=0 + 4=4\), \(y=0-2=-2\), new coordinate \((4,-2)\)

Step3: Reflect over the line \(y = x\)

The reflection rule over \(y=x\) is \((x,y)\to(y,x)\)
For \((-1,-2)\): \((-2,-1)\)
For \((3,2)\): \((2,3)\)
For \((4,2)\): \((2,4)\)
For \((4,-2)\): \((-2,4)\)

Answer:

Translation: \((-1,-2)\), \((3,2)\), \((4,2)\), \((4,-2)\)
Reflection: \((-2,-1)\), \((2,3)\), \((2,4)\), \((-2,4)\)