Lesson 1: Introduction to Cartesian Coordinates

Learning Objectives

By the end of this lesson, students will be able to:

  • Understand the structure of the Cartesian coordinate system
  • Plot points accurately on a coordinate plane
  • Identify quadrants and understand positive/negative coordinates
  • Recognize points that lie on axes
  • Interpret coordinates from a diagram and a table

The Cartesian Coordinate System

The Cartesian coordinate system uses two perpendicular number lines: - The x-axis (horizontal) - The y-axis (vertical)

The point where they intersect is called the origin, denoted as (0, 0).

Simple example of points on a Cartesian plane

Plotting Points

Each point in the plane is represented by an ordered pair (x, y): - The first number (x) tells us how far to move horizontally - The second number (y) tells us how far to move vertically

Example 1: Plotting Points

Plot the following points: - A(2, 3) - B(-1, 4) - C(-3, -2) - D(4, -1)

Coordinate basics on a grid

Example 2: Mixed Point Types

Plot each point and label it clearly:

  • E(0, 4)
  • F(5, 0)
  • G(-6, 0)
  • H(0, -3)
  • I(2, -5)
  • J(-4, 3)

Note: Points with \(x = 0\) lie on the y-axis. Points with \(y = 0\) lie on the x-axis.

Quadrants

The coordinate plane is divided into four quadrants: - Quadrant I: x > 0, y > 0 (top right) - Quadrant II: x < 0, y > 0 (top left) - Quadrant III: x < 0, y < 0 (bottom left) - Quadrant IV: x > 0, y < 0 (bottom right)

Example 2: Identifying Quadrants

In which quadrant does each point lie? - P(3, 5) → Quadrant I (both positive) - Q(-2, 7) → Quadrant II (x negative, y positive) - R(-4, -3) → Quadrant III (both negative) - S(6, -2) → Quadrant IV (x positive, y negative)

Points on the axes are not in any quadrant.

Example 3: Quadrant and Axis Check

For each point, state the quadrant or axis:

  • U(0, 7)
  • V(-8, 0)
  • W(-2, 5)
  • X(6, -1)
  • Y(3, 0)
  • Z(0, -6)

Practice Exercises

  1. Plot the following points on a coordinate plane:
    • P(3, -2)
    • Q(-4, 1)
    • R(0, 5)
    • S(-2, -3)
    • T(4, 0)
    • U(-6, 2)
    • V(5, -4)
  2. Identify the quadrant or axis for each point:
    • A(5, 7)
    • B(-3, 2)
    • C(-1, -6)
    • D(4, -3)
    • E(0, -8)
    • F(9, 0)
  3. Complete the table:
Point \(x\) value \(y\) value Quadrant/Axis
G(2, 6)
H(-5, 4)
I(0, -3)
J(-7, 0)
K(-2, -5)
  1. Name three points that lie:
    • In Quadrant II
    • On the x-axis
    • On the y-axis
  2. Create your own set of four points, one in each quadrant, and swap with a classmate to plot and check.

Worksheet 1A: Plotting Points

  1. Plot the following points on a coordinate plane:
    • A(4, 3)
    • B(-2, 5)
    • C(-3, -4)
    • D(1, -2)
    • E(0, 6)

Exit Ticket

  1. Plot and label: A(4, -2), B(-3, -1), C(0, 6).
  2. State the quadrant or axis for each point above.
  3. Write one coordinate that lies in Quadrant III and one that lies on the y-axis.

Homework

Complete the worksheet on coordinate geometry basics (see Resources).

Practice 1: P(3, -2) Q(-4, 1) R(0, 5) S(-2, -3) T(4, 0) U(-6, 2) V(5, -4)

Practice 2: A QI, B QII, C QIII, D QIV, E y-axis, F x-axis

Practice 3:

Point \(x\) value \(y\) value Quadrant/Axis
G(2, 6) 2 6 QI
H(-5, 4) -5 4 QII
I(0, -3) 0 -3 y-axis
J(-7, 0) -7 0 x-axis
K(-2, -5) -2 -5 QIII

Practice 4: Any valid points.

Practice 5: Any valid set, one in each quadrant.

Exit Ticket (sample answers): 1. Plot as given. 2. A QIV, B QIII, C y-axis. 3. Example: (-2, -4) in QIII and (0, 5) on y-axis.

Worksheet 1A answers: A QI, B QII, C QIII, D QIV, E y-axis.

Next Lesson: Lesson 2: Map It - Scale, Coordinates, and Bearings