Question

for item 2, complete each coordinate. 2. rectangle pqrs has vertices at p(-1,6), q(4,6), r(4,-2), and s(-1,-2). if pqrs is shifted 4 units to the left and 2 units up to create pqrs, what are the coordinates of the image?

Explanation:

Step1: Recall translation rule

For a left - shift of $a$ units and an up - shift of $b$ units, the transformation rule for a point $(x,y)$ is $(x - a,y + b)$. Here $a = 4$ and $b=2$.

Step2: Transform point P

For point $P(-1,6)$, using the rule $(x - 4,y + 2)$, we get $P'(-1-4,6 + 2)=P'(-5,8)$.

Step3: Transform point Q

For point $Q(4,6)$, using the rule $(x - 4,y + 2)$, we get $Q'(4-4,6 + 2)=Q'(0,8)$.

Step4: Transform point R

For point $R(4,-2)$, using the rule $(x - 4,y + 2)$, we get $R'(4-4,-2 + 2)=R'(0,0)$.

Step5: Transform point S

For point $S(-1,-2)$, using the rule $(x - 4,y + 2)$, we get $S'(-1-4,-2 + 2)=S'(-5,0)$.

Answer:

$P'(-5,8), Q'(0,8), R'(0,0), S'(-5,0)$