# Quadrilateral problems on the coordinateÂ plane

CCSS Math: 6.G.A.3
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 $A(2, 1), B(5, 1),$ and $C(5, 6)$.
What are the coordinates of point $D$?
$\large($
,
$\large)$

## 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: $A(7, 1), B(5, 1),$ $C(5, 6)$, and $D(7, 6)$.
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.
• $z$
• $x$
• $y$

## 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: $A(1,1)$, $C(4.5,4)$, and $D(-1.5,4)$. All you know about point $B$ is that it is in the first quadrant.
What are the coordinates of point $B$?
$($
$,$
$)$