Question

additional practice

1. the graph of △abc is shown. graph the image of △abc after a translation of 2 units right and 3 units up. write the coordinates of the image.

Explanation:

Step1: Identify original coordinates

Assume \(A(-3, 1)\), \(B(-4, - 2)\), \(C(-1,0)\). The rule for a translation of 2 units right and 3 units up is \((x,y)\to(x + 2,y+3)\).

Step2: Translate point A

For point \(A(-3,1)\), using the translation rule: \(x=-3,y = 1\), then \(x+2=-3 + 2=-1\), \(y + 3=1+3 = 4\). So \(A'(-1,4)\).

Step3: Translate point B

For point \(B(-4,-2)\), \(x=-4,y=-2\), then \(x + 2=-4+2=-2\), \(y+3=-2 + 3=1\). So \(B'(-2,1)\).

Step4: Translate point C

For point \(C(-1,0)\), \(x=-1,y = 0\), then \(x+2=-1+2=1\), \(y + 3=0+3=3\). So \(C'(1,3)\).

Answer:

The coordinates of the image are \(A'(-1,4)\), \(B'(-2,1)\), \(C'(1,3)\)