Question

draw the following triangle after a translation 2 units to the left and 3 units up.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ in the coordinate - plane, a translation 2 units to the left and 3 units up changes the point to $(x - 2,y+3)$.

Step2: Identify triangle vertices

Let the vertices of the original triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$.

Step3: Apply translation to vertices

The new vertices will be $(x_1 - 2,y_1 + 3),(x_2 - 2,y_2 + 3),(x_3 - 2,y_3 + 3)$.

Step4: Plot new triangle

Use the new vertices to draw the translated triangle on the coordinate - plane.

Answer:

Draw the triangle with vertices obtained by applying the translation $(x,y)\to(x - 2,y + 3)$ to the original triangle's vertices.