Question

1. examine the figure below, translate the pre - image (x,y)→(x + 3,y - 2), be sure to correctly label all points.

Explanation:

Step1: Identify original coordinates

Let's assume \(A=(3,3)\), \(B=(1,2)\), \(C=(2,1)\)

Step2: Apply translation rule to point A

For \(A=(3,3)\), using the rule \((x,y)\to(x + 3,y - 2)\), we have \(x=3,y = 3\). Then \(x+3=3 + 3=6\) and \(y - 2=3-2 = 1\). So the new - coordinates of \(A\) are \((6,1)\).

Step3: Apply translation rule to point B

For \(B=(1,2)\), with \(x = 1,y = 2\), \(x+3=1+3 = 4\) and \(y - 2=2-2=0\). So the new - coordinates of \(B\) are \((4,0)\).

Step4: Apply translation rule to point C

For \(C=(2,1)\), with \(x = 2,y = 1\), \(x+3=2+3 = 5\) and \(y - 2=1-2=-1\). So the new - coordinates of \(C\) are \((5,-1)\).

Step5: Plot and label new points

Plot the points \(A'(6,1)\), \(B'(4,0)\), \(C'(5,-1)\) on the coordinate - plane and label them correctly.

Answer:

The new coordinates of \(A\) are \((6,1)\), of \(B\) are \((4,0)\) and of \(C\) are \((5,-1)\) which should be plotted and labeled on the coordinate - plane.