Question

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

Explanation:

Step1: Recall translation rule

For a translation $a$ units to the left and $b$ units down, the rule for a point $(x,y)$ is $(x - a,y - b)$. Here $a = 4$ and $b=4$.

Step2: Identify original points

Assume the vertices of the triangle are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. For example, if one vertex is $(0,4)$, after translation 4 units to the left and 4 units down, the new - point is $(0 - 4,4 - 4)=(-4,0)$. Do this for all vertices of the triangle.

Step3: Plot new - triangle

Connect the new points obtained from the translation to form the new triangle.

Since this is a graphical problem and we can't actually draw in this text - based format, the steps above describe how to perform the translation. If we were to assume the vertices of the original triangle are $(0,4),(2,2),(-2,-4)$:

• For the point $(0,4)$: New point is $(0 - 4,4 - 4)=(-4,0)$.
• For the point $(2,2)$: New point is $(2 - 4,2 - 4)=(-2,-2)$.
• For the point $(-2,-4)$: New point is $(-2 - 4,-4 - 4)=(-6,-8)$.

Answer:

Plot the triangle with vertices obtained by applying the translation $(x,y)\to(x - 4,y - 4)$ to the original triangle's vertices.