Question

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

Explanation:

Step1: Recall rotation rules

• 90° clockwise: \((x,y)\to(y, -x)\)
• 90° counter - clockwise: \((x,y)\to(-y,x)\)
• 180°: \((x,y)\to(-x,-y)\)
• 270° clockwise: \((x,y)\to(-y,x)\)
• 270° counter - clockwise: \((x,y)\to(y, -x)\)

Step2: Check the transformation

Take \(G(-2,7)\) as an example.
If we use the rule for \(270^{\circ}\) clockwise rotation:
For a point \((x,y)\), the image is \((-y,x)\).
When \(x = - 2\) and \(y=7\), \(-y=-7\) and \(x=-2\), the image is \((-7,-2)\) which matches \(G'\).
Check \(H(-4,8)\): \(-y=-8\), \(x = - 4\), image is \((-8,-4)\) which matches \(H'\).
Check \(I(-3,5)\): \(-y=-5\), \(x=-3\), image is \((-5,-3)\) which matches \(I'\).

Answer:

270 degrees clockwise