Question

the coordinates of the vertices of a quadrilateral are n (2, 1), p (2, -2), q (-1, -1), and r (-1, 2). quadrilateral npqr is translated 5 units to the left and 4 units down to create quadrilateral npqr. what are the coordinates of the vertices of quadrilateral npqr? n = p =

Explanation:

Step1: Recall translation rule

For a translation 5 units left and 4 units down, the rule for a point $(x,y)$ is $(x - 5,y - 4)$.

Step2: Find coordinates of $N'$

Given $N(2,1)$, using the rule: $x=2,y = 1$, then $x'=2 - 5=-3,y'=1 - 4=-3$. So $N'(-3,-3)$.

Step3: Find coordinates of $P'$

Given $P(2,-2)$, using the rule: $x = 2,y=-2$, then $x'=2 - 5=-3,y'=-2 - 4=-6$. So $P'(-3,-6)$.

Step4: Find coordinates of $Q'$

Given $Q(-1,-1)$, using the rule: $x=-1,y=-1$, then $x'=-1 - 5=-6,y'=-1 - 4=-5$. So $Q'(-6,-5)$.

Step5: Find coordinates of $R'$

Given $R(-1,2)$, using the rule: $x=-1,y = 2$, then $x'=-1 - 5=-6,y'=2 - 4=-2$. So $R'(-6,-2)$.

Answer:

$N'=(-3,-3)$
$P'=(-3,-6)$
$Q'=(-6,-5)$
$R'=(-6,-2)$