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# Quadrilateral problems on the coordinate plane

Try five problems involving quadrilaterals on the coordinate plane.

## Problem 1: Find coordinates of missing vertex

The coordinates of three of the vertices of rectangle $ABCD$ are $A\left(2,1\right),B\left(5,1\right),$ and $C\left(5,6\right)$.
What are the coordinates of point $D$?
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,
$\right)$

## Problem 2: Area of parallelogram on coordinate plane

Find the area of the parallelogram plotted below.
units${}^{2}$

## Problem 3: Dimensions of rectangle from coordinates

Rectangle $ABCD$ is graphed in the coordinate plane. The following are the vertices of the rectangle: $A\left(7,1\right),B\left(5,1\right),$ $C\left(5,6\right)$, and $D\left(7,6\right)$.
Given these coordinates, what is the length of side $AD$ of this rectangle?
units

## Problem 4: Coordinates of rectangle

Sort the following expressions from least to greatest based on the coordinates of the rectangle below.

## Bonus problem: Parallelogram on the coordinate plane

You are graphing quadrilateral $ABCD$ in the coordinate plane. The length of segment $AB$ is the same as the length of segment $DC$, and both segments are horizontal. The following are three vertices of the quadrilateral: $A\left(1,1\right)$, $C\left(4.5,4\right)$, and $D\left(-1.5,4\right)$. All you know about point $B$ is that it is in the first quadrant.
What are the coordinates of point $B$?
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$,$
$\right)$