Question

1. graph the image of trapezoid bcde after a reflection over the y - axis and a translation 5 units up and 2 units right.

Explanation:

Step1: Find coordinates of original points

Assume \( B(1,-3)\), \(C(2,-2)\), \(D(4,-3)\), \(E(2,-5)\)

Step2: Reflect over \(y\) - axis

Use the rule \((x,y)\to(-x,y)\).
For \(B(1,-3)\): \((1,-3)\to B'(-1,-3)\)
For \(C(2,-2)\): \((2,-2)\to C'(-2,-2)\)
For \(D(4,-3)\): \((4,-3)\to D'(-4,-3)\)
For \(E(2,-5)\): \((2,-5)\to E'(-2,-5)\)

Step3: Translate 5 units up and 2 units right

Use the rule \((x,y)\to(x + 2,y+5)\)
For \(B'(-1,-3)\): \((-1+2,-3 + 5)\to B''(1,2)\)
For \(C'(-2,-2)\): \((-2+2,-2 + 5)\to C''(0,3)\)
For \(D'(-4,-3)\): \((-4+2,-3 + 5)\to D''(-2,2)\)
For \(E'(-2,-5)\): \((-2+2,-5 + 5)\to E''(0,0)\)

Answer:

Plot the points \(B''(1,2)\), \(C''(0,3)\), \(D''(-2,2)\), \(E''(0,0)\) and connect them to form the image of the trapezoid.