Question

given the graph of \\( \triangle rst \\), find the coordinates of the \\( \triangle rst \\).

• reflection about the \\( y = x \\) line, followed by \\( (x, y) \to (x + 10, y - 2) \\)

\\( r(\square, \square) \\)
\\( s(\square, \square) \\)
\\( t(\square, \square) \\)

Explanation:

Step1: Find original coordinates

From the graph, assume \(R(6, - 2)\), \(S(1,-1)\), \(T(3,-4)\)

Step2: Reflection about \(y = x\)

The rule for reflection about \(y=x\) is \((x,y)\to(y,x)\).
For \(R(6,-2)\): \((6,-2)\to(-2,6)\)
For \(S(1,-1)\): \((1,-1)\to(-1,1)\)
For \(T(3,-4)\): \((3,-4)\to(-4,3)\)

Step3: Translation \((x,y)\to(x + 10,y-2)\)

For the reflected point of \(R\): \((-2+10,6 - 2)=(8,4)\)
For the reflected point of \(S\): \((-1 + 10,1-2)=(9,-1)\)
For the reflected point of \(T\): \((-4+10,3 - 2)=(6,1)\)

Answer:

\(R''(8,4)\), \(S''(9,-1)\), \(T''(6,1)\)