Question

1. determine which points are the remaining vertices of a rectangle with a perimeter of 14 units.

a a(2, - 2) and b(2, - 1)
b c(-2, - 2) and d(-2, 2)
c e(-2, - 2) and f(2, - 2)
d g(2, 0) and h(-2, 0)

Explanation:

Step1: Recall rectangle perimeter formula

$P = 2(l + w)$ where $P$ is perimeter, $l$ is length and $w$ is width. Given $P=14$, then $l + w=7$.

Step2: Analyze option A

Points $A(2,-2)$ and $B(2,-1)$ have the same $x -$coordinate. Distance $AB=\vert-2-(-1)\vert = 1$. But we can't form a rectangle with other points to get perimeter 14.

Step3: Analyze option B

Points $C(-2,-2)$ and $D(-2,2)$ have the same $x -$coordinate. Distance $CD=\vert-2 - 2\vert=4$. If we try to form a rectangle, we can't get $l + w = 7$.

Step4: Analyze option C

Points $E(-2,-2)$ and $F(2,-2)$ have the same $y -$coordinate. Distance $EF=\vert-2 - 2\vert = 4$. Let one side be 4, then the other side $s$ from $l + w=7$ is $s = 3$. But we can't form a rectangle with given points to get perimeter 14.

Step5: Analyze option D

Points $G(2,0)$ and $H(-2,0)$ have the same $y -$coordinate. Distance $GH=\vert2-(-2)\vert=4$. Let one side be 4, then the other side $s$ from $l + w = 7$ is $s=3$. If we consider a rectangle with vertices, we can form a rectangle with perimeter $2(4 + 3)=14$.

Answer:

D. $G(2,0)$ and $H(-2,0)$