Question

draw the image of $\triangle abc$ under a translation by 5 units to the left.

Explanation:

Step1: Identify vertices of △ABC

From the graph:
$A(-1, 1)$, $B(1, -3)$, $C(3, 0)$

Step2: Apply left translation rule

Subtract 5 from each x-coordinate:
$A'(-1-5, 1) = (-6, 1)$
$B'(1-5, -3) = (-4, -3)$
$C'(3-5, 0) = (-2, 0)$

Step3: Plot and connect new vertices

Plot $A'(-6,1)$, $B'(-4,-3)$, $C'(-2,0)$, then connect them to form $\triangle A'B'C'$.

Answer:

The vertices of the translated triangle are $A'(-6, 1)$, $B'(-4, -3)$, $C'(-2, 0)$. When plotted and connected, this forms the image of $\triangle ABC$ translated 5 units left.