Question

3a) triangle abc has a=(3,1), b=(1,5), c=(5,3). graph abc = r_{(0,0),90^{circ}}(t_{(-6,1)}(abc)). neither abc nor abc will fit on this grid.

Explanation:

Step1: Translation formula

The translation \(T_{(h,k)}(x,y)=(x + h,y + k)\). Here \(h=-6,k = 1\).
For point \(A(3,1)\): \(T_{(-6,1)}(3,1)=(3-6,1 + 1)=(-3,2)\)
For point \(B(1,5)\): \(T_{(-6,1)}(1,5)=(1-6,5 + 1)=(-5,6)\)
For point \(C(5,3)\): \(T_{(-6,1)}(5,3)=(5-6,3 + 1)=(-1,4)\)

Step2: Rotation formula

The rotation \(R_{(0,0),90^{\circ}}(x,y)=(-y,x)\)
For the translated point \(A'(-3,2)\): \(R_{(0,0),90^{\circ}}(-3,2)=(-2,-3)\)
For the translated point \(B'(-5,6)\): \(R_{(0,0),90^{\circ}}(-5,6)=(-6,-5)\)
For the translated point \(C'(-1,4)\): \(R_{(0,0),90^{\circ}}(-1,4)=(-4,-1)\)

Answer:

The coordinates of \(A''(-2,-3)\), \(B''(-6,-5)\) and \(C''(-4,-1)\)