Question

graph the image of parallelogram fghi after the following sequence of transformations:
translation 17 units down
rotation 90° counterclockwise around the origin

Explanation:

Step1: Find coordinates of original points

From the graph, the coordinates are \(F(-8,9)\), \(G(-2,7)\), \(H(-2,3)\), \(I(-8,5)\).

Step2: Translate 17 units down

The translation rule for moving \(17\) units down is \((x,y)\to(x,y - 17)\).

• For \(F(-8,9)\): \((-8,9-17)=(-8,-8)\)
• For \(G(-2,7)\): \((-2,7 - 17)=(-2,-10)\)
• For \(H(-2,3)\): \((-2,3-17)=(-2,-14)\)
• For \(I(-8,5)\): \((-8,5 - 17)=(-8,-12)\)

Step3: Rotate 90° counter - clockwise around the origin

The rotation rule for \(90^{\circ}\) counter - clockwise around the origin is \((x,y)\to(-y,x)\).

• For \(F'(-8,-8)\): \((-(-8),-8)=(8,-8)\)
• For \(G'(-2,-10)\): \((-(-10),-2)=(10,-2)\)
• For \(H'(-2,-14)\): \((-(-14),-2)=(14,-2)\)
• For \(I'(-8,-12)\): \((-(-12),-8)=(12,-8)\)

Answer:

Plot the points \((8,-8)\), \((10,-2)\), \((14,-2)\), \((12,-8)\) and connect them to form the image of the parallelogram after the given sequence of transformations.