Question

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

Explanation:

Step1: Recall translation rule

A translation 1 unit left and 6 units up means subtract 1 from the x - coordinate and add 6 to the y - coordinate of each point.

Step2: Identify coordinates of $\triangle ABC$

Let's assume $A(-5,1)$, $B(-5,3)$, $C(-2, - 1)$.

Step3: Apply translation to point A

For point $A(-5,1)$: New x - coordinate is $-5 - 1=-6$, new y - coordinate is $1 + 6 = 7$. So new $A'(-6,7)$.

Step4: Apply translation to point B

For point $B(-5,3)$: New x - coordinate is $-5 - 1=-6$, new y - coordinate is $3+6 = 9$. So new $B'(-6,9)$.

Step5: Apply translation to point C

For point $C(-2,-1)$: New x - coordinate is $-2 - 1=-3$, new y - coordinate is $-1 + 6 = 5$. So new $C'(-3,5)$.

Step6: Graph new triangle

Plot points $A'(-6,7)$, $B'(-6,9)$ and $C'(-3,5)$ and connect them to form the new triangle.

Answer:

Graph the triangle with vertices $A'(-6,7)$, $B'(-6,9)$ and $C'(-3,5)$ on the given coordinate - plane.