Question

draw the following triangle after a translation 3 units to the right and 1 unit down.

Explanation:

Step1: Identify the vertices of the original triangle

Assume the vertices of the original triangle are \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\).

Step2: Apply the translation rule

The translation rule for moving 3 units to the right (add 3 to the \(x\)-coordinate) and 1 unit down (subtract 1 from the \(y\)-coordinate) is \((x,y)\to(x + 3,y-1)\).
So the new vertices are \((x_1+3,y_1 - 1)\), \((x_2+3,y_2 - 1)\), \((x_3+3,y_3 - 1)\).

Step3: Plot the new vertices and draw the triangle

Using the new vertices \((x_1+3,y_1 - 1)\), \((x_2+3,y_2 - 1)\), \((x_3+3,y_3 - 1)\), plot them on the coordinate - plane and connect them to form the translated triangle.

Answer:

Follow the above steps to draw the translated triangle.