Question

the coordinates of triangle abc are, a (1,-2), b(-3,6) and (4,5). what are the coordinates of the vertices of its image after the transformation ( t_{2,-1} circ r_{y - axis} )? (3,-3),(-1,5),(6,4) (-1,-2),(3,6),(-4,5) (3,1),(-1,7),(6,-6) (1,-3),(5,5),(-2,4)

Explanation:

Step1: Find the coordinates after reflection about the \(y -\)axis

The rule for reflection about the \(y -\)axis is \((x,y)\to(-x,y)\).
For point \(A(1, - 2)\): \((1,-2)\to(-1,-2)\)
For point \(B(-3,6)\): \((-3,6)\to(3,6)\)
For point \(C(4,5)\): \((4,5)\to(-4,5)\)

Step2: Find the coordinates after translation \(T_{2,-1}\)

The rule for translation \(T_{2,-1}\) is \((x,y)\to(x + 2,y-1)\)
For the reflected point \((-1,-2)\): \((-1+2,-2 - 1)=(1,-3)\)
For the reflected point \((3,6)\): \((3 + 2,6-1)=(5,5)\)
For the reflected point \((-4,5)\): \((-4+2,5 - 1)=(-2,4)\)

Answer:

\((1,-3),(5,5),(-2,4)\)