Question

draw the image of △abc under the translation (x,y)→(x - 6,y - 7).

Explanation:

Step1: Identify coordinates of vertices

Let's assume \(A=(4,4)\), \(B=(7,0)\), \(C=(2,2)\) from the graph.

Step2: Apply translation rule to point A

For \(A=(4,4)\), using \((x,y)\to(x - 6,y - 7)\), we get \(A'=(4-6,4 - 7)=(-2,-3)\).

Step3: Apply translation rule to point B

For \(B=(7,0)\), using \((x,y)\to(x - 6,y - 7)\), we get \(B'=(7-6,0 - 7)=(1,-7)\).

Step4: Apply translation rule to point C

For \(C=(2,2)\), using \((x,y)\to(x - 6,y - 7)\), we get \(C'=(2-6,2 - 7)=(-4,-5)\).

Step5: Plot the new triangle

Plot points \(A'(-2,-3)\), \(B'(1,-7)\) and \(C'(-4,-5)\) and connect them to form \(\triangle A'B'C'\).

Answer:

Plot points \(A'(-2,-3)\), \(B'(1,-7)\), \(C'(-4,-5)\) and connect them to get the image of \(\triangle ABC\) under the given translation.