Lesson 15

Shapes on the Coordinate Plane

Let’s use the coordinate plane to solve problems and puzzles.

15.1: Figuring Out The Coordinate Plane

  1. Draw a figure in the coordinate plane with at least three of following properties:
    • 6 vertices

    • 1 pair of parallel sides

    • At least 1 right angle

    • 2 sides the same length

  2. Is your figure a polygon? Explain how you know.

15.2: Plotting Polygons

Here are the coordinates for four polygons. Move the slider to choose the polygon you want to plot. Move the points, in order, to their locations on the coordinate plane. Sketch each one before changing the slider.

  1. Polygon 1: \((\text-7, 4), (\text-8, 5), (\text-8, 6), (\text-7, 7), (\text-5, 7), (\text-5,5), (\text-7, 4)\)

  2. Polygon 2: \((4, 3), (3, 3), (2, 2), (2, 1), (3, 0), (4, 0), (5, 1), (5, 2), (4, 3)\)

  3. Polygon 3: \((\text-8, \text-5), (\text-8, \text-8), (\text-5, \text-8), (\text-5, \text-5), (\text-8, \text-5)\)

  4. Polygon 4: \((\text-5, 1), (\text-3, \text-3), (\text-1, \text-2), (0, 3), (\text-3, 3), (\text-5, 1)\)



Find the area of Polygon D in this activity.

15.3: Four Quadrants of A-Maze-ing

  1. The following diagram shows Andre’s route through a maze. He started from the lower right entrance.

    A maze on a coordinate plane.  Please ask for additional help.
    1. What are the coordinates of the first two and the last two points of his route?
    2. How far did he walk from his starting point to his ending point? Show how you know.
  2. Jada went into the maze and stopped at \((\text-7, 2)\).

    1. Plot that point and other points that would lead her out of the maze (through the exit on the upper left side).
    2. How far from \((\text-7, 2)\) must she walk to exit the maze? Show how you know.

Summary

We can use coordinates to find lengths of segments in the coordinate plane. 

Coordinate plane, origin O, axes labeled by ones.

For example, we can find the perimeter of this polygon by finding the sum of its side lengths. Starting from \((\text-2, 2)\) and moving clockwise, we can see that the lengths of the segments are 6, 3, 3, 3, 3, and 6 units. The perimeter is therefore 24 units. 

In general:

  • If two points have the same \(x\)-coordinate, they will be on the same vertical line, and we can find the distance between them.
  • If two points have the same \(y\)-coordinate, they will be on the same horizontal line, and we can find the distance between them.

Glossary Entries

  • quadrant

    The coordinate plane is divided into 4 regions called quadrants. The quadrants are numbered using Roman numerals, starting in the top right corner.

    A coordinate plane, origin O. The area top & right of the origin is Quadrant 1, and counter-clockwise labeled quadrant 2, 3, 4.