Question

the vertices of a quadrilateral are p( - 1, - 1), q(0,4), r(3,1), and s(1, - 2). draw the figure and its image after a translation 3 units left and 2 units up.

Explanation:

Step1: Recall translation rule

For a translation $3$ units left and $2$ units up, the rule for a point $(x,y)$ is $(x - 3,y + 2)$.

Step2: Translate point P

For $P(-1,-1)$, substitute $x=-1$ and $y = - 1$ into the rule: $(-1-3,-1 + 2)=(-4,1)$.

Step3: Translate point Q

For $Q(0,4)$, substitute $x = 0$ and $y=4$ into the rule: $(0-3,4 + 2)=(-3,6)$.

Step4: Translate point R

For $R(3,1)$, substitute $x = 3$ and $y = 1$ into the rule: $(3-3,1 + 2)=(0,3)$.

Step5: Translate point S

For $S(1,-2)$, substitute $x = 1$ and $y=-2$ into the rule: $(1-3,-2 + 2)=(-2,0)$.

Answer:

The vertices of the image are $P'(-4,1),Q'(-3,6),R'(0,3),S'(-2,0)$