Question

draw the image of △abc under a translation by 5 units to the left.

Explanation:

Step1: Recall translation rule

For a translation 5 units to the left, subtract 5 from the x - coordinate of each vertex.

Step2: Identify vertices of △ABC

Let \(A=(0,1)\), \(B=(1, - 3)\), \(C=(3,0)\).

Step3: Calculate new vertices

For point \(A\): New \(x=0 - 5=-5\), \(y = 1\), so \(A'=(-5,1)\).
For point \(B\): New \(x=1 - 5=-4\), \(y=-3\), so \(B'=(-4,-3)\).
For point \(C\): New \(x=3 - 5=-2\), \(y = 0\), so \(C'=(-2,0)\).

Step4: Draw new triangle

Plot points \(A'(-5,1)\), \(B'(-4,-3)\) and \(C'(-2,0)\) on the coordinate - plane and connect them to form the image of \(\triangle ABC\).

Answer:

Plot points \(A'(-5,1)\), \(B'(-4,-3)\) and \(C'(-2,0)\) and connect them to get the translated triangle.