Question

analyze the pre - image abcd. what are the vertices of the final image if $t_{-1,-2}circ r_{y = x}$ is applied to figure abcd? a\ b\(3, 2) c\ d\ (1, -1) (-1,1) (0,1) (1,0)

Explanation:

Step1: Identify pre - image vertices

From the graph, assume \(A(1,4)\), \(B(3,4)\), \(C(3,2)\), \(D(1,2)\)

Step2: Apply reflection \(r_{y = x}\)

The rule for reflection over the line \(y=x\) is \((x,y)\to(y,x)\). So \(A(1,4)\to A'(4,1)\), \(B(3,4)\to B'(4,3)\), \(C(3,2)\to C'(2,3)\), \(D(1,2)\to D'(2,1)\)

Step3: Apply translation \(T_{- 1,-2}\)

The rule for translation \(T_{-1,-2}\) is \((x,y)\to(x - 1,y - 2)\). So \(A'(4,1)\to A''(4-1,1 - 2)=(3,-1)\), \(B'(4,3)\to B''(4 - 1,3 - 2)=(3,1)\), \(C'(2,3)\to C''(2-1,3 - 2)=(1,1)\), \(D'(2,1)\to D''(2 - 1,1 - 2)=(1,-1)\)

Answer:

A''(3,-1)
C''(1,1)
D''(1,-1)