Question

what are the coordinates of a, b, and c after a translation to the right by 4 units and up 1 unit? plot these points on the grid, and label them a, b and c.

Explanation:

Step1: Determine original coordinates

The original coordinates of point $A$ are $(-6,5)$, of point $B$ are $(3,2)$ and of point $C$ are $(0, - 1)$.

Step2: Apply translation rule

The translation rule for moving right by 4 units and up by 1 unit is $(x,y)\to(x + 4,y+1)$.
For point $A(-6,5)$:
$x=-6,y = 5$, then $x+4=-6 + 4=-2,y + 1=5+1 = 6$. So $A'$ has coordinates $(-2,6)$.
For point $B(3,2)$:
$x = 3,y=2$, then $x + 4=3+4=7,y+1=2 + 1=3$. So $B'$ has coordinates $(7,3)$.
For point $C(0,-1)$:
$x = 0,y=-1$, then $x+4=0 + 4=4,y+1=-1+1=0$. So $C'$ has coordinates $(4,0)$.

Answer:

$A'(-2,6),B'(7,3),C'(4,0)$