# Basics Of Coordinate Geometry

## Coordinates

Before looking at coordinate geometry, you will have to know what coordinates are. The table on the right
is a very simplified version of a coordinate grid. In coordinate geometry, the coordinates are written in the
format (x,y). X is the value on the x (horizontal) axis and y is the value on the y (vertical) axis. On the grid
on the right there are 3 marked coordinates:
•
Red cross: (1,1)
•
Blue cross: (3,2)
•
Green cross: (2,4)
On an actual coordinate plane, the coordinates will be a bit different but the basic concept is the same.
## The Coordinate Plane

Above you can see a typical coordinate plane. The y axis is the vertical axis and the x axis is the horizontal one. On the middle of the coordinate plane
is the origin (0,0). In the top right section, both coordinates are positive while in the bottom left section both coordinates will be negative. One point has
been plotted on the coordinate plane (3,2). 3 is the x and 2 the y value.
## Basic Functions (y=mx+c)

The standard form of a straight line function
is y=mx+c. Where m is the gradient and c is
the y-intercept. The graph on the right shows
the function:
(1)x stands for the gradient: 1. This means
that for every time we move right one, we
move up one. The higher the x value, the
steeper the slope of the line. +1 is the y
intercept. This is the y value at which the line
cuts the y axis.
Here are some more basic functions plotted on graphs. See if you can see the relationships between the gradient (mx) and the y-intercept (c).

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y-axis
(horizontal)

origin
(0,0)

x-axis
(vertical)

Point
(3,2)

1

1

y-intercept (0,1)

In this graph we have a gradient of two. For every one you go across, you go
up two. The y-intercept is at 2.

In this graph we have a gradient of a half. For every one you go across, you
go up a half. The y-intercept is at the origin (0,0).

## Functions with Negative Gradients

Functions can also have negative gradients. This is shown in the graph underneath.
The function for this equation is . For every time we go across one, we go down one. The line intercepts the y-axis at -1. Underneath
are a couple of examples with negatives functions.
In this graph we have a gradient of negative two. For every one you go
across, you go down two. The y-intercept is at 1.

In this graph we have a gradient of negative one and a half. For every one
you go across, you go down one and a half. The y-intercept is at the origin
-2.

## Advanced Coordinate Geometry

You should now be familiar with the basics of coordinate geometry. Now you can study some more advanced aspects such as mid point and distance
between points. Please share this page if you like it or found it helpful!

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Chapter 35.1: Learning Outcomes
Students will be introduced to the concept of coordinates!
Students will learn how to use and interpret the coordinate planes!
Students will learn about basic functions!

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