Draw Polygons in the Coordinate Plane

6.G.A.3

In this lesson:

• Plot vertices and draw polygons in all four quadrants
• Find side lengths using absolute value
• Solve real-world problems involving coordinate polygons

Your Three Learning Goals for Today

By the end of this lesson, you should be able to:

1. Plot vertices as ordered pairs and connect them to draw the specified polygon
2. Find the length of a side joining two vertices that share an - or -coordinate using absolute value
3. Apply coordinate side length calculations to real-world problems including perimeter

What You Already Know About Coordinates

You can already plot and read points in all four quadrants:

• A point like means: move 3 left, 2 up
• All four quadrants — positive and negative values
• Absolute value gives distance from zero:

Today we connect multiple points to create polygons.

Drawing Polygons: The Three Steps

To draw a polygon from its vertex coordinates:

1. Plot each vertex on the coordinate plane
2. Connect the vertices in the given order: A→B→C→D→...
3. Close the polygon by connecting the last vertex back to the first

The order matters — connecting wrong creates a crossed, invalid shape.

Plotting a Rectangle from Given Vertices

Vertices: , , , — a rectangle spanning all four quadrants.

Measuring Sides with Absolute Value

For sides that are horizontal or vertical, use:

• Horizontal side (same -coordinate): length
• Vertical side (same -coordinate): length

Check first: do the two points share an or value?
If neither coordinate is shared — the side is diagonal.

Rectangle Side Lengths and Perimeter

Using the rectangle , , , :

Perimeter =

Quick Check: Choosing the Right Formula

For each segment, decide: use or ?

1. to
2. to
3. to

Think through each one before the next slide...

Checking Your Formula Choices: Revealed

1. to : same →
2. to : same →
3. to : diagonal — no shared coordinate → length cannot be found at Grade 6

Right Triangle with a Diagonal Side

• Vertical leg:
• Horizontal leg:
• Hypotenuse: diagonal — cannot compute at Grade 6

Practice Problem: Finding L-Shape Perimeter

An L-shaped hexagon has vertices:
, , , , ,

1. Plot and connect these vertices in order
2. Find each of the six side lengths
3. Calculate the perimeter

Try it before the next slide...

L-Shape Practice: Full Solution Revealed

Perimeter =

From Coordinates to Real-World Context

In Chunk 2, coordinates often represent real-world locations:

• Units carry meaning (feet, meters, miles)
• The perimeter represents a real distance to walk, fence, or build
• Always include units in your answer and interpret in context

The same calculation skills apply — just with real meaning attached.

Worked Example: Measuring a Neighborhood Park

Park vertices: , , ,

• Width: units
• Height: units
• Perimeter = units

Practice: Draw and Measure a Garden

A garden has vertices: , , , , ,

1. Draw the garden on a coordinate grid
2. Find each side length using absolute value
3. Calculate the perimeter of the garden

Try it before the next slide...

Garden Practice: Full Perimeter Solution

Perimeter = units

Summary: Key Ideas from This Lesson

✓ Plot vertices, connect in order, close the polygon (last → first)

✓ Horizontal side (same ): length

✓ Vertical side (same ): length

Connect in listed order — connecting by proximity creates a crossed shape

Diagonal sides cannot be measured at Grade 6 (no shared coordinate)

Always close the polygon — last vertex connects back to first

Preview: Area of Coordinate Plane Polygons

Coming up: Area of polygons in the coordinate plane

• Same coordinate skills, now computing enclosed area
• Rectangular polygons: area = length × width
• Composite figures: break into rectangles, add areas
• Connection to 6.G.A.1 (area of polygons)