draw the image of △abc under a translation by 2 units down.

Explanation:

Step1: Recall translation rule

For a translation 2 units down, subtract 2 from the y - coordinate of each vertex while keeping the x - coordinate the same.

Step2: Identify vertices of △ABC

Let's assume the vertices of △ABC are (A(x_1,y_1)), (B(x_2,y_2)), (C(x_3,y_3)). From the graph, if (A=(2, - 4)), (B=(0,-5)), (C=(6,2)).

Step3: Apply translation

For point (A): New (y) - coordinate is (y_1 - 2=-4 - 2=-6), new point (A'=(2,-6)). For point (B): New (y) - coordinate is (y_2 - 2=-5 - 2=-7), new point (B'=(0,-7)). For point (C): New (y) - coordinate is (y_3 - 2=2 - 2 = 0), new point (C'=(6,0)).

Step4: Draw the new triangle

Plot the points (A'), (B'), and (C') on the coordinate - plane and connect them to form the new triangle (\triangle A'B'C').

Answer:

Plot the points (A'(2,-6)), (B'(0,-7)), (C'(6,0)) and connect them to get the image of (\triangle ABC) under the given translation.