Represent Polygons on the Coordinate Plane

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems, explain what each part stands for, and build one for a situation I have not seen before.

The big idea: When two vertices share a coordinate, the side between them is the absolute difference of the coordinates that differ — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me find one side

(-4.5, 3) and (5, 3) share y = 3, so the side between them is horizontal.
Its length is the distance between the x-coordinates: |5 − (−4.5)| = 9.5 units.
(5, 3) and (5, -3.75) share x = 5, so that side is vertical: |3 − (−3.75)| = 6.75 units.

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: The shape is a rectangle, so the opposite sides match: two sides of 9.5 and two of 6.75. Perimeter = 2(9.5) + 2(6.75) = 19 + 13.5 = 32.5 units. That is why two of the terms are multiplied by 2 — each length appears on two sides. Now prove it: say why that move had to work at all — not just that it did.
Show your work

6.NOS.9 Group 2 · Challenge

Practice Set · Part 2

Represent Polygons on the Coordinate Plane

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

2
Think it throughThe two known vertices of the park are 3 units apart, and each grid unit represents 100 feet. What is the park's width in feet?
1. A300 feet
2. B3 feet
3. C103 feet
4. D30 feet
Why is that the answer?
3
Think it throughThe park's area must be 240,000 sq ft and its width is 300 ft. What is its length?
1. A800 feet
2. B80,000 feet
3. C720 feet
4. D240,300 feet
How do you know? Give a second reason as well.
4
Think it throughThe park's length is 800 feet, and each grid unit represents 100 feet. How many units below the known vertices do the new corners sit?
1. A8 units
2. B80 units
3. C800 units
4. D0.8 units
Explain your thinking. What would have to change for a different choice to be right?
5
Back to the modelThe vertices (-4.5, 3) and (5, 3) share y = 3, so the side between them is horizontal, with length |5 − (−4.5)| = 9.5. Why is that side's length found by comparing the x-coordinates instead of the y-coordinates?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

A — Same x or same y — subtract coordinatesB — Slanted — coordinates alone won't give it yet

(2, 5) and (2, -3)
(-4, 1) and (6, 1)
(0, 0) and (4, 3)
(-4.5, 3) and (5, 3)
(1, 2) and (5, 7)
(5, 3) and (5, -3.75)
(-2, -2) and (3, 4)
(7, -1) and (-3, -1)

6.NOS.9 Group 2 · Challenge

Practice Set · Part 3

Represent Polygons on the Coordinate Plane

Words and reasoning

Word bank · Banco de palabras

vertex (vértice)polygon (polígono)perimeter (perímetro)distance between vertices (distancia entre vértices)scale (escala)

Use the words

Fill each blank with a word from the bank.

A corner point of a polygon, named by an ordered pair, is a ___.
A closed figure made of line segments is a ___.
The total distance around a polygon is its ___.
When two vertices share a coordinate, subtract the other and take the ___ ___.

Explain the thinking

6
Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.
The mistake: Subtracting coordinates without the absolute value — from y = 3 down to y = −3.
7
Say moreYou sorted pairs of vertices into 'subtract coordinates' versus 'slanted.' How did you decide that (0, 0) and (4, 3) belonged in the slanted group?
8
Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A town-planning map shows a grid with two corner points of a future rectangular park already marked. The rest of the park is drawn only as a dashed outline waiting for its other two corners.
Show your work

6.NOS.9 Group 2 · Challenge

Practice Set · Part 4

Represent Polygons on the Coordinate Plane

Show what you know

Last check

These two come from Lesson 7.6. If they are shaky, that is the lesson to revisit — not this one.

9
Show what you knowExplain your thinking — A rectangle has vertices (-1, 4), (5, 4), (5, 1), (-1, 1). What is its perimeter?
1. A18 units
2. B9 units
3. C6 units
4. D18 square units
Explain your choice.
10
From Lesson 7.6Explain your thinking — What is the distance between the points (3, -2) and (3, 5)?
1. A3 units
2. B5 units
3. C7 units
4. D9 units
How do you know?
11
From Lesson 7.6What is the total flight path?
1. A12 units
2. B2 units
3. C35 units
4. D7 units
How do you know?

Be honest — this tells your teacher what to do next

I can…	Not yet	Getting there	Got it
I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems, explain what each part stands for, and build one for a situation I have not seen before.
I can explain why it works: When two vertices share a coordinate, the side between them is the absolute difference of the coordinates…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time