Question

is this figure defined by points e, f, g, and h a rectangle? justify your answer.
○ no, efgh is not a rectangle. based on the coordinates, opposite sides are parallel but not congruent.
○ no, efgh is not a rectangle. based on the coordinates, opposite sides are congruent but not parallel.
○ yes, efgh is a rectangle. base on the coordinates, opposite sides are neither parallel nor congruent.
○ yes, efgh is a rectangle. base on the coordinates, opposite sides are both parallel and congruent.

Explanation:

Step1: Identify point coordinates

From the grid: $E=(8, -12)$, $F=(12, -12)$, $G=(12, -6)$, $H=(8, -6)$

Step2: Calculate side lengths

Length of $EF$: $|12-8| = 4$
Length of $FG$: $|-6-(-12)| = 6$
Length of $GH$: $|12-8| = 4$
Length of $HE$: $|-6-(-12)| = 6$

Step3: Check parallelism

$EF$ and $GH$ are horizontal (constant $y$-value), so parallel.
$FG$ and $HE$ are vertical (constant $x$-value), so parallel.

Step4: Verify rectangle criteria

Opposite sides are parallel and congruent, and all angles are right angles (from horizontal/vertical sides).

Answer:

Yes, EFGH is a rectangle. Base on the coordinates, opposite sides are both parallel and congruent.