Question

13
a triangle has vertices ( a(-1,2) ), ( b(2,5) ), and ( c(3,-4) ). if the image resulting from a rotation has vertices ( a(2,1) ), ( b(5,-2) ), and ( c(-4,-3) ), describe the rotation using coordinates. * (10 points)
( (x,y)\to(y,-x) )
( (x,y)\to(-y,-x) )
( (x,y)\to(-x,-y) )
( (x,y)\to(-y,x) )

Explanation:

Step1: Check each transformation rule for point A

For \(A(-1,2)\):

• For \((x,y)\to(y, -x)\): \((-1,2)\to(2,1)\)
• For \((x,y)\to(-y,-x)\): \((-1,2)\to(-2,1)\)
• For \((x,y)\to(-x,-y)\): \((-1,2)\to(1,-2)\)
• For \((x,y)\to(-y,x)\): \((-1,2)\to(-2,-1)\)

Step2: Check each transformation rule for point B

For \(B(2,5)\):

• For \((x,y)\to(y, -x)\): \((2,5)\to(5,-2)\)
• For \((x,y)\to(-y,-x)\): \((2,5)\to(-5,-2)\)
• For \((x,y)\to(-x,-y)\): \((2,5)\to(-2,-5)\)
• For \((x,y)\to(-y,x)\): \((2,5)\to(-5,2)\)

Step3: Check each transformation rule for point C

For \(C(3,-4)\):

• For \((x,y)\to(y, -x)\): \((3,-4)\to(-4,-3)\)
• For \((x,y)\to(-y,-x)\): \((3,-4)\to(4,-3)\)
• For \((x,y)\to(-x,-y)\): \((3,-4)\to(-3,4)\)
• For \((x,y)\to(-y,x)\): \((3,-4)\to(4,3)\)

Answer:

\((x, y)\to(y, -x)\)