Unit 7, Lesson 11
Points in the Coordinate Plane
Grade 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?
11.2
Activity
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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. - Plot a point at . Label it .
- Plot another point at . Label it .
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The coordinate plane is divided into four quadrants: I, II, III, and IV, as shown here.
In which quadrant is point located? Point ? Point ? - If a point has a positive -coordinate, in which quadrants could it be?
11.3
Activity
Here is an image of an archery target on a coordinate grid. The scores for landing an arrow in each of the regions are shown.
- A: 10 points
- B: 8 points
- C: 6 points
- D: 4 points
- E: 2 points
Name the possible coordinates of where one arrow could land to earn each of the following scores:
- 6 points
- 10 points
- 2 points
- no points
- 4 points
- 8 points
Student Lesson Summary
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 . The - and -coordinates for point are positive, so is to the right of the -axis and above the -axis. Point is located in Quadrant I.
The - and -coordinates for point are negative, so is to the left of the -axis and below the -axis. Point is located in Quadrant III.
Quadrant IV contains points whose -coordinates are positive and whose -coordinates are negative.
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 .