Question

1. r 6, -2, o 4, 0, x 3, -3 translated left three units and up two units.

r
o
x
algebraic rule:

Explanation:

Step1: Recall translation rule

The rule for translating a point $(x,y)$ left $a$ units and up $b$ units is $(x - a,y + b)$. Here $a = 3$ and $b=2$.

Step2: Translate point R(6,-2)

For point $R(6,-2)$, using the rule $(x - 3,y + 2)$, we have $x=6,y = - 2$. Then $x-3=6 - 3=3$ and $y + 2=-2 + 2=0$. So $R'=(3,0)$.

Step3: Translate point O(4,0)

For point $O(4,0)$, with $x = 4,y = 0$, then $x-3=4 - 3=1$ and $y + 2=0+2 = 2$. So $O'=(1,2)$.

Step4: Translate point X(3,-3)

For point $X(3,-3)$, with $x = 3,y=-3$, then $x - 3=3-3 = 0$ and $y+2=-3 + 2=-1$. So $X'=(0,-1)$.

Answer:

$R':(3,0)$
$O':(1,2)$
$X':(0,-1)$
Algebraic Rule: $(x,y)\to(x - 3,y + 2)$