Coordinates

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What is the Cartesian Plane?

The Cartesian plane is a flat, two-dimensional grid that helps us locate points precisely. Think of it like a map with two number lines crossing each other.

The Cartesian plane has two main parts:

• x-axis: This is the horizontal line (goes left and right)
• y-axis: This is the vertical line (goes up and down)

These two axes meet at a special point called the origin, where both x and y equal zero. The origin is labeled as (0, 0).

Understanding Coordinates

Coordinates are a pair of numbers that tell us exactly where a point is on the Cartesian plane. They work like an address for a location on the grid.

How coordinates are written:

• Coordinates are always written inside brackets as (x, y)
• The first number is the x-coordinate (horizontal position)
• The second number is the y-coordinate (vertical position)
• The order matters! Always write x first, then y

A helpful phrase to remember: "Along the corridor, up the stairs" - this reminds you to move horizontally first (x), then vertically (y).

Understanding positive and negative values:

The origin divides the plane into four sections, and coordinates can be positive or negative depending on where they are:

• Positive x-values: Points to the right of the origin
• Negative x-values: Points to the left of the origin
• Positive y-values: Points above the origin
• Negative y-values: Points below the origin

Examples:

• (3, 5) means: start at the origin, move 3 units to the right, then 5 units up
• (-2, 4) means: start at the origin, move 2 units to the left, then 4 units up
• (1, -3) means: start at the origin, move 1 unit to the right, then 3 units down
• (-4, -2) means: start at the origin, move 4 units to the left, then 2 units down

Reading Coordinates from a Graph

When you need to find the coordinates of a point already marked on a grid:

Step 1: Look at how far the point is to the left or right of the origin

• If it's to the right, the x-coordinate is positive
• If it's to the left, the x-coordinate is negative

Step 2: Look at how far the point is above or below the origin

• If it's above, the y-coordinate is positive
• If it's below, the y-coordinate is negative

Step 3: Count the number of units in each direction

Step 4: Write your answer in brackets as (x, y)

Important note: Always check the scale on the grid! Sometimes one square on the grid represents more than one unit. Look carefully at the numbers labeled on the axes.

Plotting Coordinates on a Graph

When you need to plot (mark) a point on a grid when given coordinates:

Step 1: Start at the origin (0, 0)

Step 2: Use the x-coordinate to move horizontally

• If x is positive, move right
• If x is negative, move left

Step 3: Use the y-coordinate to move vertically

• If y is positive, move up
• If y is negative, move down

Step 4: Mark the point with a clear dot or cross, and label it if required

Example: To plot the point (4, -3):

• Start at the origin
• Move 4 units to the right (because x = 4)
• Move 3 units down (because y = -3)
• Mark the point clearly