Question

draw the following triangle after a translation 3 units to the right and 4 units up.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ in the coordinate - plane, a translation 3 units to the right and 4 units up changes the point to $(x + 3,y+4)$.

Step2: Identify vertices of the original triangle

Let's assume the vertices of the original triangle are $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$. From the graph, if one vertex is at $(-2,4)$, another at $(2,2)$ and the third at $(-2,-3)$.

Step3: Apply the translation rule to each vertex

For the vertex $(-2,4)$: $x=-2,y = 4$, the new vertex is $(-2 + 3,4 + 4)=(1,8)$.
For the vertex $(2,2)$: $x = 2,y=2$, the new vertex is $(2+3,2 + 4)=(5,6)$.
For the vertex $(-2,-3)$: $x=-2,y=-3$, the new vertex is $(-2 + 3,-3 + 4)=(1,1)$.

Step4: Draw the new triangle

Plot the new vertices $(1,8)$, $(5,6)$ and $(1,1)$ on the coordinate - plane and connect them to form the translated triangle.

Answer:

Draw a triangle with vertices at $(1,8)$, $(5,6)$ and $(1,1)$ on the given coordinate - plane.