Question

draw the following triangle after a translation 2 units to the left and 4 units down.

Explanation:

Step1: Find the original coordinates

Assume the vertices of the triangle have coordinates \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\). For a translation 2 units to the left (subtract 2 from the \(x\) - coordinate) and 4 units down (subtract 4 from the \(y\) - coordinate).
The translation rule is \((x,y)\to(x - 2,y - 4)\)

Step2: Calculate the new coordinates

If a vertex has coordinate \((x,y)\), after translation, its new coordinate is \((x-2,y - 4)\). For example, if one vertex is \((-2,2)\), after translation, it becomes \((-2-2,2 - 4)=(-4,-2)\); if another vertex is \((0,0)\), after translation, it becomes \((0 - 2,0-4)=(-2,-4)\); if the third vertex is \((2,-2)\), after translation, it becomes \((2-2,-2 - 4)=(0,-6)\)

Step3: Plot the new triangle

Connect the points with the new coordinates \((x-2,y - 4)\) for each vertex of the original triangle.

Answer:

Plot the points obtained from applying the translation rule \((x,y)\to(x - 2,y - 4)\) to each vertex of the original triangle and then connect them to form the translated triangle.