Question

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

Explanation:

Step1: Identify coordinates of vertices

Let \(A=(4,4)\), \(B=(7,0)\), \(C=(2,2)\)

Step2: Apply translation to \(x - \)coordinate

For point \(A\), new \(x\) - coordinate is \(4 - 6=-2\); for \(B\), new \(x\) - coordinate is \(7 - 6 = 1\); for \(C\), new \(x\) - coordinate is \(2-6=-4\)

Step3: Apply translation to \(y - \)coordinate

For point \(A\), new \(y\) - coordinate is \(4 - 7=-3\); for \(B\), new \(y\) - coordinate is \(0 - 7=-7\); for \(C\), new \(y\) - coordinate is \(2 - 7=-5\)

Step4: Plot new vertices

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

Answer:

Plot points \(A'(-2,-3)\), \(B'(1,-7)\), \(C'(-4,-5)\) and draw \(\triangle A'B'C'\)