Question

triangle abc was transformed to create triangle abc.
choose the algebraic description using coordinates to describe the transformation of triangle abc used to create triangle abc.
algebraic description: (x, y)→

Explanation:

Step1: Find coordinates of points

Let's assume coordinates of \(A=(1,1)\), \(B=(1,4)\), \(C=(3,1)\) in \(\triangle ABC\) and \(A'=(-1, - 2)\), \(B'=(-1,-5)\), \(C'=(-3,-2)\) in \(\triangle A'B'C'\)

Step2: Analyze \(x\) - coordinate change

For \(x\) - coordinate: \(1\to - 1\), \(1\to - 1\), \(3\to - 3\). The rule for \(x\) is \(x\to -x\)

Step3: Analyze \(y\) - coordinate change

For \(y\) - coordinate: \(1\to - 2\), \(4\to - 5\), \(1\to - 2\). The rule for \(y\) is \(y\to y - 3\)

Answer:

\((x,y)\to(-x,y - 3)\)