Question

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.

Step2: Identify vertices of △ABC

Let the vertices of △ABC be \(A(x_A,y_A)\), \(B(x_B,y_B)\), \(C(x_C,y_C)\). From the graph, assume \(A(2,- 4)\), \(B(0,-5)\), \(C(6,2)\).

Step3: Calculate new vertices

For point \(A\): \(y_A'=y_A - 2=-4 - 2=-6\), \(x_A'=x_A = 2\), so \(A'(2,-6)\).
For point \(B\): \(y_B'=y_B - 2=-5 - 2=-7\), \(x_B'=x_B = 0\), so \(B'(0,-7)\).
For point \(C\): \(y_C'=y_C - 2=2 - 2 = 0\), \(x_C'=x_C = 6\), so \(C'(6,0)\).

Step4: Draw new triangle

Plot the points \(A'(2,-6)\), \(B'(0,-7)\) and \(C'(6,0)\) on the same coordinate - grid and connect them to form the new triangle.

Answer:

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