Question

practice

1. triangle ( b a t ) has vertices ( b(2,1), a(6,2) ), and ( t(3,6) ). if ( \triangle b a t ) is transformed by a rotation

of ( 270^{circ} ) counterclockwise about the origin followed by a translation with rule ( (x, y)
ightarrow ) ( (x+ ) ( 3, y+6) ), what will be the coordinates of the final image after the two transformations?
a. ( (2,-6) )
b. ( (5,0) )
c. ( (6,-3) )
d. ( (9,3) )

Explanation:

Step1: Rotation formula

The formula for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\).
For point \(B(2,1)\): After rotation, \(B_1=(1,-2)\)
For point \(A(6,2)\): After rotation, \(A_1=(2,-6)\)
For point \(T(3,6)\): After rotation, \(T_1=(6,-3)\)

Step2: Translation formula

The translation rule is \((x,y)\to(x + 3,y+6)\)
For \(B_1=(1,-2)\): \(B_2=(1 + 3,-2+6)=(4,4)\)
For \(A_1=(2,-6)\): \(A_2=(2 + 3,-6 + 6)=(5,0)\)
For \(T_1=(6,-3)\): \(T_2=(6+3,-3 + 6)=(9,3)\)

Answer:

B. \((5,0)\)