Question

pentagon abcde is shown on the graph. draw the resulting image after it is reflected across the x - axis and translated up 2 units.

Explanation:

Step1: Find coordinates of original pentagon

Assume coordinates: \(A(4,8)\), \(B(2,7)\), \(C(2,4)\), \(D(7,5)\), \(E(6,7)\)

Step2: Reflect across x - axis

The rule for reflection across the \(x\) - axis is \((x,y)\to(x, - y)\).
So new coordinates: \(A'(4, - 8)\), \(B'(2, - 7)\), \(C'(2, - 4)\), \(D'(7, - 5)\), \(E'(6, - 7)\)

Step3: Translate up 2 units

The rule for translation up \(2\) units is \((x,y)\to(x,y + 2)\).
Final coordinates: \(A''(4,-8 + 2)=(4,-6)\), \(B''(2,-7 + 2)=(2,-5)\), \(C''(2,-4+2)=(2,-2)\), \(D''(7,-5 + 2)=(7,-3)\), \(E''(6,-7 + 2)=(6,-5)\)

Step4: Plot the new points

Connect the points \(A''(4,-6)\), \(B''(2,-5)\), \(C''(2,-2)\), \(D''(7,-3)\), \(E''(6,-5)\) to form the new pentagon.

Answer:

Plot the points \((4,-6)\), \((2,-5)\), \((2,-2)\), \((7,-3)\), \((6,-5)\) and connect them to get the required pentagon.