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Unit 7 · Standard 6.GR.3

Represent Polygons on the Coordinate Plane

Lesson 7-7 · Learn It — how the math works

Why we're learning this

A polygon's vertices are given as coordinates: (-4.5, 3), (5, 3), (5, -3.75), and (-4.5, -3.75). What is its perimeter?

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The coordinates already know the side lengths

Graph the points, connect them in order, and the polygon appears. Then the same coordinates that placed the corners tell you exactly how long each side is.

Picture itSee what the math looks like before you read about it

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.
Where you see this in real lifeA 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.

Watch me solve itI do — read one step at a time

The problem looks like this
Coordinate plane: the side from (−4.5, 3) to (5, 3) is horizontal and 9.5 units long; the side from (5, 3) to (5, −3.75) is vertical and 6.75 units long.−6−5−4−3−2−1123456−5−4−3−2−1123450xy(−4.5, 3)(5, 3)(5, −3.75)
  1. (-4.5, 3) and (5, 3) share y = 3, so the side between them is horizontal.
  2. Its length is the distance between the x-coordinates: |5 − (−4.5)| = 9.5 units.
  3. (5, 3) and (5, -3.75) share x = 5, so that side is vertical: |3 − (−3.75)| = 6.75 units.

Watch out — mistakes students make here

  • 6 is only the width, from x = −1 to x = 5. Perimeter goes around all four sides: 6 + 3 + 6 + 3.
  • 9 is the width plus the height, 6 + 3 — only two of the four sides. Add the other two sides as well.
  • 3 is the number of UNITS — the scale turns units into feet.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. The shape is a rectangle, so the opposite sides match: two sides of 9.5 and two of 6.75.
  2. = 2(9.5) + 2(6.75) = 19 + 13.5 = 32.5 units.
  3. That is why two of the terms are multiplied by 2 — each length appears on two sides.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • A square has vertices (1, 2), (6, 2), (6, -3), (1, -3). Find one from the coordinates, then the .
  • Say which pair of vertices you used and why their shared coordinate mattered.

Solve: The park's marked vertices are 3 units apart and each unit is 100 feet. What is the park's width?

My answer

Stuck? Open one hint at a time.

Hint 1

What does one unit stand for?

Hint 2

Each unit is 100 feet.

Hint 3

3 × 100.

Check my answer
✅ Answer: 300 feet
3 units × 100 feet per unit = 300 feet.

Turn & TalkSay it out loud with a partner

The 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?

Try starting with:

  • The side is horizontal because both vertices share the same ___-coordinate.El lado es horizontal porque ambos vértices comparten la misma coordenada ___.
  • I subtract the ___-coordinates because that's the coordinate that ___.Resto las coordenadas ___ porque esa es la coordenada que ___.
Use these wordsvertexcoordinatesdistance between vertices