Question

graph the image of △abc after a translation 1 unit left and 6 units up.

Explanation:

Step1: Recall translation rule

The rule for a translation 1 unit left and 6 units up is $(x,y)\to(x - 1,y + 6)$.

Step2: Identify coordinates of $\triangle ABC$

Let's assume $A(-6,1)$, $B(-6,3)$, $C(-2,-1)$.

Step3: Apply translation rule to point A

For point $A(-6,1)$, $x=-6,y = 1$. After translation, $x'=-6-1=-7,y'=1 + 6=7$. So $A'(-7,7)$.

Step4: Apply translation rule to point B

For point $B(-6,3)$, $x=-6,y = 3$. After translation, $x'=-6-1=-7,y'=3 + 6=9$. So $B'(-7,9)$.

Step5: Apply translation rule to point C

For point $C(-2,-1)$, $x=-2,y=-1$. After translation, $x'=-2-1=-3,y'=-1 + 6=5$. So $C'(-3,5)$.

Step6: Graph the new triangle

Plot points $A'(-7,7)$, $B'(-7,9)$ and $C'(-3,5)$ and connect them to form the translated $\triangle A'B'C'$.

Answer:

Graph the points $A'(-7,7)$, $B'(-7,9)$ and $C'(-3,5)$ and connect them to get the image of $\triangle ABC$ after the given translation.