If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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 A, B, C, D are A, left parenthesis, 2, comma, 1, right parenthesis, comma, B, left parenthesis, 5, comma, 1, right parenthesis, comma and C, left parenthesis, 5, comma, 6, right parenthesis.
What are the coordinates of point D?
left parenthesis
,
right parenthesis

## Problem 2: Area of parallelogram on coordinate plane

Find the area of the parallelogram plotted below.
unitssquared

## Problem 3: Dimensions of rectangle from coordinates

Rectangle A, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A, left parenthesis, 7, comma, 1, right parenthesis, comma, B, left parenthesis, 5, comma, 1, right parenthesis, comma C, left parenthesis, 5, comma, 6, right parenthesis, and D, left parenthesis, 7, comma, 6, right parenthesis.
Given these coordinates, what is the length of side A, D 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 A, B, C, D in the coordinate plane. The length of segment A, B is the same as the length of segment D, C, and both segments are horizontal. The following are three vertices of the quadrilateral: A, left parenthesis, 1, comma, 1, right parenthesis, C, left parenthesis, 4, point, 5, comma, 4, right parenthesis, and D, left parenthesis, minus, 1, point, 5, comma, 4, right parenthesis. All you know about point B is that it is in the first quadrant.
What are the coordinates of point B?
left parenthesis
comma
right parenthesis