Unit 7, Lesson 11
Constructing the Coordinate Plane
Accelerated 6
11.1
Warm-up
Choose 1 set of points, and write the coordinates of each of the 3 points in the set. What do you notice about the coordinates?
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Choose 1 set of points, and write the coordinates of each of the 3 points in the set. What do you notice about the coordinates?
Write the coordinates of each labeled point.
Coordinate plane, negative 7 to 7 by ones on the horizontal axis, negative 5 to 5 on the vertical axis. Point A is 3 units to the right and 4 units up from the origin. Point B is 7 units to the left and 2 units down from Point A. Point C is 1 unit to the left and 5 units down from Point B. Point D is 9 units to the right and 1 unit up from Point C.
The coordinate plane is divided into four quadrants: I, II, III, and IV, as shown here.
In which quadrant is point located? Point ? Point ?
For each set of coordinates, draw and label an appropriate pair of axes, and plot the points.
Discuss with a partner:
Here is a maze in a coordinate plane. The black point in the center is (0, 0). The side of each grid square is 2 units long.
The starting point of the maze is located at the top left of the maze and labeled as point . Draw line segments to show your way through and out of the maze. Label each turning point with a letter. Then list all the letters, and write their coordinates.
Just as the number line can be extended to the left to include negative numbers, the - and -axes can also be extended to include negative values. This creates the coordinate plane, a system that can be used to describe the locations of points.
For example, point can be described by the ordered pair . The -value of -4 tells us that the point is 4 units to the left of the -axis. The -value of 1 tells us that the point is 1 unit above the -axis. Point is located in Quadrant II.
The same reasoning applies to the points and . Point is located in Quadrant I. Point is located in Quadrant III.
Quadrant IV contains points whose -coordinates are positive and whose -coordinates are negative.
The coordinate plane can also be used to show information involving pairs of numbers. When using the coordinate plane, we should pay close attention to what each axis represents and what scale each axis uses.
Suppose we want to plot the following points: , , , and .
The data involve whole numbers, so it is appropriate that each square on the grid represents a whole number.
Here is a possible graph of the data.
Coordinate plane, origin O, horizontal axis, time in hours after midnight, negative 8 to 10 by ones, vertical axis, temperature in degrees celsius, negative 8 to 6 by ones. Points at (negative 4 comma 30), (negative 1 comma negative 2), (zero comma negative 4), (3 comma negative 8).
The coordinate plane is one way to represent pairs of numbers. The plane is made of a horizontal number line and a vertical number line that cross at 0.
Pairs of numbers can be used to describe the location of a point in the coordinate plane.
Point is located at . This means is 3 units to the right and 2 units down from .
The coordinate plane is divided into 4 sections called quadrants. The quadrants are numbered using Roman numerals, as shown.