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### Course: 8th grade foundations (Eureka Math/EngageNY)>Unit 7

Lesson 2: Topic C: Foundations

# 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 $D$?
$\left($
,
$\right)$

## 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 $B$?
$\left($
$,$
$\right)$

## Want to join the conversation?

• 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 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.
• what is the answer to life
• 17. The answer is always 17.
• How do you do this I don't understand the parraellograms
• That is not how you spell parallelograms
(1 vote)
• why is this so increasingly difficult bruh
• it gets increasingly difficult because now that we're getting older, the education system expects us to do MORE.

I feel you, bro.
(1 vote)
• Hey guys

I'm taking Geometry this coming fall, so I'm trying to prepare by taking the Khan courses, "Geometry" and "Get ready for Geometry." The course "Get ready for Geometry" is a bit easy right now, so I'm wondering if I should skip it and jump to the course "Geometry." What do you guys think? Is "Get ready for Geometry" vital for the course "Geometry"?
• Sorry, I think I posted in the wrong section, so I'll repeat just in case: I think the "Get ready for Geometry" is pretty useful, but I don't think it's vital if you understand most of the concepts already.🙃
(1 vote)
• All qustions should come wit a coordinate grid!