Lesson 15Shapes on the Coordinate Plane

Learning Goal

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

Learning Targets

  • I can find the lengths of horizontal and vertical segments in the coordinate plane.

  • I can plot polygons on the coordinate plane when I have the coordinates for the vertices.

Warm Up: Figuring Out The Coordinate Plane

Problem 1

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

    open applet in presentation mode

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

Print Version

  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

    A coordinate plane with the origin labeled “O”. The numbers 0 through 18 are indicated on the horizontal axis and the numbers 0 through 14 are indicated on the vertical axis.

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

Activity 1: Plotting Polygons

Problem 1

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.

  • Polygon 1:

  • Polygon 2:

  • Polygon 3:

  • Polygon 4:

open applet in presentation mode
Print Version

Here are the coordinates for four polygons. Plot them on the coordinate plane, connect the points in the order that they are listed, and label each polygon with its letter name.

  • Polygon A:

  • Polygon B:

  • Polygon C:

  • Polygon D:

A coordinate plane with the origin labeled “O”. The numbers negative 10 through 10, in increments of 2, are indicated on the horizontal axis and the numbers negative 8 through 8, in increments of 2, are indicated on the vertical axis.

Are you ready for more?

Problem 1

Find the area of Polygon D in this activity.

Activity 2: Four Quadrants of A-Maze-ing

Problem 1

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

A maze on a coordinate plane. Andre's route through the maze is shown in red. The coordinates of the four corners are: (-11, 15), (-11, -15), (11, -15) (11, 15).

  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.

Problem 2

Jada went into the maze and stopped at .

open applet in presentation mode

  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 must she walk to exit the maze? Show how you know.

Print Version

Jada went into the maze and stopped at .

  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 must she walk to exit the maze? Show how you know.

Lesson Summary

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

A 6-sided polygon is drawn on a coordinate plane with the origin labeled "O". The numbers negative 7 through 7 are indicated on the horizontal axis. The numbers negative 6 through 6 are indicated on the vertical axis. Starting from the first vertex and moving clockwise, the six vertices of the polygon are as follows: Negative 2 comma 2. 4 comma 2. 4 comma negative 1. 1 comma negative 1. 1 comma negative 4. Negative 2 comma negative 4.

For example, we can find the perimeter of this polygon by finding the sum of its side lengths. Starting from 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 -coordinate, they will be on the same vertical line, and we can find the distance between them.

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