Question

a triangle has vertices at ( a(1,3) ), ( b(4,2) ) and ( c(3,8) ). which transformation would produce an image with vertices ( a(3,-1),b(2,-4),c(8,-3) )?

• a rotation ( 90^{circ} ) counterclockwise
• a reflection over the ( y )-axis
• a reflection over the ( x )-axis
• a rotation ( 90^{circ} ) clockwise

Explanation:

Step1: Recall rotation rules

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

Step2: Apply the rule to each vertex

For \(A(1,3)\):
Using the rule \((x,y)\to(y, -x)\), we get \((1,3)\to(3,-1)\) which is \(A'\).
For \(B(4,2)\):
Using the rule \((x,y)\to(y, -x)\), we get \((4,2)\to(2,-4)\) which is \(B'\).
For \(C(3,8)\):
Using the rule \((x,y)\to(y, -x)\), we get \((3,8)\to(8,-3)\) which is \(C'\).

Answer:

a rotation \(90^{\circ}\) clockwise