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
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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:
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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:
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.
What are the coordinates of the first two and the last two points of his route?
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
Plot that point and other points that would lead her out of the maze (through the exit on the upper left side).
How far from
must she walk to exit the maze? Show how you know.
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Jada went into the maze and stopped at
Plot that point and other points that would lead her out of the maze (through the exit on the upper left side).
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.
For example, we can find the perimeter of this polygon by finding the sum of its side lengths. Starting from
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.