Lesson 11: Points in the Coordinate Plane

Points in the Coordinate Plane

Student Summary

Just as the number line can be extended to the left to include negative numbers, the $x$ - and $y$ -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.

Coordinate plane, x and y axis, origin O, points marked and labeled. A = (2 comma 3), B = (negative 4 comma 1), C = (negative 3 point 5 comma negative 3).

For example, point $B$ can be described by the ordered pair $(\text-4,1)$ . The $x$ -value of -4 tells us that the point is 4 units to the left of the $y$ -axis. The $y$ -value of 1 tells us that the point is 1 unit above the $x$ -axis. Point $B$ is located in Quadrant II.

The same reasoning applies to the points $A$ and $C$ . The $x$ - and $y$ -coordinates for point $A$ are positive, so $A$ is to the right of the $y$ -axis and above the $x$ -axis. Point $A$ is located in Quadrant I.

The $x$ - and $y$ -coordinates for point $C$ are negative, so $C$ is to the left of the $y$ -axis and below the $x$ -axis. Point $C$ is located in Quadrant III.

Quadrant IV contains points whose $x$ -coordinates are positive and whose $y$ -coordinates are negative.

Visual / Anchor Chart

Standards

Building On

5.G.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system.

Addressing

6.NS.6.b

Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.

6.NS.6.c

Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.

6.NS.8

Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Building Toward

6.NS.6

Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.

6.NS.8