Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
14.2
Activity
Signs of Numbers in Coordinates
Standards Alignment
Building On
Addressing
6.NS.6.b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Coordinate plane, origin O, horizontal axis negative 7 through 7 by ones, vertical axis negative 5 through 5 by ones. Point A is 4 units to the right of the origin and 3 units up. Point B is 6 units down from point A. Point C is 1 unit to the left and 2 units down from point B. Point D is 7 units to the left and 2 units up from point C. Point E is 2 units to the left and 6 units up from point D.
Answer these questions for each pair of points.
How are the coordinates the same? How are they different?
How far away are they from the -axis? To the left or to the right of it?
How far away are they from the -axis? Above or below it?
and
and
and
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Plot point in the coordinate plane, and label it with its coordinates.
How far away are and from the -axis?
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Plot point in the coordinate plane, and label it with its coordinates.
How far away are and from the -axis?
Point has the same coordinates as point , except both coordinates have opposite signs. In which quadrant is point ?
14.3
Activity
Finding Distances in a Coordinate Plane
Standards Alignment
Building On
Addressing
6.NS.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Coordinate plane, origin O, hoizontal axis negative 7 through 7 by ones, vertical axis negative 5 through 5 by ones. Point A is 1 point 5 units to the left and 2 units up from the origin. Point B is 5 units to the right of point A. Point C is 5 units to the right and 5 units down from point A. Point D is 5 units to the right and 6 point 5 units down from point A. Point E is 6 point 5 units directly below point A.
Find the distance between each pair of points.
Points and
Points and
Points and
Which of the points are 5 units from ?
Which of the points are 2 units from ?
Plot a point that is both 2.5 units from and 9 units from . Label that point , and write down its coordinates.
Student Lesson Summary
The points , and are shown in the coordinate plane. Notice that they all have almost the same coordinates, except the signs are different. They are all the same distance from each axis but are in different quadrants.
Notice that the vertical distance between points and is 4 units because point is 2 units above the horizontal axis and point is 2 units below the horizontal axis. The horizontal distance between points and is 10 units because point is 5 units to the left of the vertical axis and point is 5 units to the right of the vertical axis.
We can always tell which quadrant a point is located in by the signs of its coordinates.
quadrant
positive
positive
I
negative
positive
II
negative
negative
III
positive
negative
IV
Glossary
None
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Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.