What is a Coordinate Plane?; X-axis, Y-axis, and Origin; Understanding Ordered Pairs; How to Plot Points; How to Find Coordinates

Coordinate Geometry Basics

Mathematics

Coordinate Geometry Basics

Learn to find exact locations using coordinate geometry.

Agenda

• What is a Coordinate Plane?

• X-axis, Y-axis, and Origin

• Understanding Ordered Pairs

• How to Plot Points

• How to Find Coordinates

Finding Places with Math

Coordinate geometry helps us find exact locations, just like finding a hidden treasure on a map. It's like giving directions using numbers and letters. We use it to pinpoint places on a grid, similar to playing a game like Battleship.

Locating points and shapes on a coordinate grid.

What is a Coordinate Plane?

Imagine a special flat surface, like a piece of graph paper. We use this plane to show exact locations, just like finding a spot on a map. It helps us organize points using numbers.

Coordinate systems map locations on a flat surface using numbers.

The X-Axis: Horizontal Line

• The x-axis is the flat line going across.

• It's like a number line for left and right.

• Numbers to the right are positive (1, 2, 3).

• Numbers to the left are negative (-1, -2, -3).

The Y-Axis: Vertical Line

• The y-axis is the vertical line.

• It measures positions up and down.

• Positive numbers go up (like a balloon).

• Negative numbers go down (like a submarine).

Where They Meet: The Origin

Imagine two straight roads crossing each other perfectly in the middle. This special meeting spot, like the center of a map, is called the origin in coordinate geometry. It's always marked by the coordinates (0,0), meaning zero steps right or left, and zero steps up or down.

Origin (0,0): The starting point in coordinate geometry.

Understanding Ordered Pairs

An ordered pair is like a special address for a point on a map! It uses two numbers, (x, y), to tell us exactly where to find something. The first number, x, tells you how far to go left or right, and the second number, y, tells you how far to go up or down. For example, (3, 2) means go 3 units right, then 2 units up.

Ordered pairs locate points on a line in analytic geometry.

Locating point (2, 4) in the first quadrant.

First Number: X-Coordinate

• First number in (x, y) is the x-coordinate.

• Shows how far to move left or right.

• Move right for positive x-values.

• Move left for negative x-values.

Second Number: Y-Coordinate

• The second number is the Y-coordinate.

• It tells you how far to move UP or DOWN.

• Move UP for positive Y, DOWN for negative Y.

• Example: (3, 5) means move 5 units UP.

Step 1: Start at Origin

When you plot a point on a coordinate plane, your journey always begins at the origin. Think of it like the starting line in a race, located at (0,0). This central spot is where the X-axis and Y-axis meet, like the center of a map.

Step 2: Move Along X-Axis

After starting at the origin (0,0), your next step is to move horizontally along the x-axis. The first number in your ordered pair, like the '3' in (3, 5), tells you how many steps to take right or left. You move right if the x-coordinate is positive, and left if it is negative.

Step 3: Move Along Y-Axis

After finding your spot on the x-axis, the next step is to move up or down. Look at the y-coordinate to decide: if it's positive, move up from your current position. If it's negative, move down. For example, from (3,0), a y-coordinate of 4 means move up 4 steps to reach (3,4).

Step 4: Mark the Point

After moving right for the x-coordinate and up for the y-coordinate, you've found your spot. Now, simply place a clear dot right there to mark your point. For example, if you moved to (3, 4), put your dot at that exact intersection.

Practice Plotting: Point A

Let's practice plotting Point A (3, 2) on our coordinate grid. Start at the origin (0,0). The first number, 3, tells us to move 3 steps to the right. Then, the second number, 2, tells us to move 2 steps up and mark your point.

Coordinate Geometry Basics

What is a Coordinate Plane?; X-axis, Y-axis, and Origin; Understanding Ordered Pairs; How to Plot Points; How to Find Coordinates

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