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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 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

## Want to join the conversation?

• how do you do the bonus problum?
• First, calculate the length of segment DC. X-axis of point D to C = -1.5 + s = 4.5 and y-axis of point D to C = 4+t=4. Then we got the length s is 6 and the length t is 0.
(Remember length in the segment is length between two-point. s and t is just a variable to represent the length in x-axis and y-axis of segment DC.)
Since the length of segment AB is the same as the length of segment DC---> X-axis of point A to B = 1 + 6 = j and Y-axis of point A to B = 1 + 0 = k ---> B(j , k) =B(7 , 1).
Sorry for my English. Hope this helps.
• why is the alphabet now on math
• the letters aren't considered as the alphabet in the problems they are just used to show the different points and they also use the letters to name the points so that you don't get confused.
• How do you do this I don't understand the parraellograms
• To solve it easily, you first have to find the length of the base, or the long side. You also should find the height, and it is the distance from the long side to the other long side. After you find those dimensions, solve the rest like how you would solve for the area of an rectangle and square.
(1 vote)
• i just wanna say hello
• I did a unit test and it did not test all of the skills inside that unit (6th Grade Geometry). Why weren't all of the skills tested as it was supposed to be a unit test?
• Sometimes, there are not enough questions in the Unit Test to level you up in all of the skills. You might have to take the Unit Test more than once to reach your mastery goal.
• Im so confused.
• I need help with problem 2 pls :(