Question

which description of a rotation matches the table shown?
pre - image\timage
g(-2,7)\tg(-7,-2)
h(-4,8)\th(-8,-4)
i(-3,5)\ti(-5,-3)
270 counterclockwise
270 degrees clockwise
180 counterclockwise
90 degrees clockwise
clear my selection

Explanation:

Step1: Recall rotation rules

• For a \(90^{\circ}\) clockwise rotation \((x,y)\to(y, -x)\)
• For a \(180^{\circ}\) rotation \((x,y)\to(-x,-y)\)
• For a \(270^{\circ}\) clockwise rotation \((x,y)\to(-y,x)\)
• For a \(270^{\circ}\) counter - clockwise rotation \((x,y)\to(y, -x)\)

Take the point \(G(-2,7)\) as an example.
If we consider a \(270^{\circ}\) counter - clockwise rotation:
Using the rule \((x,y)\to(y, -x)\), for \(G(-2,7)\), we get \((7,2)\) (not correct).
If we consider a \(270^{\circ}\) clockwise rotation:
Using the rule \((x,y)\to(-y,x)\), for \(G(-2,7)\), we get \((-7,-2)\)
Check for \(H(-4,8)\): Using the \(270^{\circ}\) clockwise rotation rule \((x,y)\to(-y,x)\), we have \((-8,-4)\)
Check for \(I(-3,5)\): Using the \(270^{\circ}\) clockwise rotation rule \((x,y)\to(-y,x)\), we have \((-5,-3)\)

Answer:

270 degrees clockwise