# Advanced Coordinate Geometry

## Introduction

In this lesson, you will learn some more advanced coordinate geometry skills such as gradient, mid-point and distance between two points.
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To calculate the gradient of a line one a coordinate plane you can use the following equation. Take 2 points on the line and substitute                and               . m is equal to the gradient. Have a look at how the gradient is calculate for the line underneath. On this line we have identified two points (-1,-1) and (0,2). We can now substitute the values into the formula to find the gradient. The gradient is 3. We could use this to find the equation of the line: y=3x+2.

## Mid-Point

We use the following formula to calculate the mid-point of a line connecting two points. Take the two end points                and                 and substitute the x and y values into the equation to determine the mid-point. Have a look at the example underneath. The two points are (6,3) and (-6,-3). Let us now substitute these values into the equation. The mid-point in this case is the origin (0,0).

## Distance Between Two Points

To calculate the distance between two points on a coordinate plane, we use the following formula. Again we need to to take the two points                and               and substitute the values into the formula. This has been done in the example underneath. The two points are (4,3) and (-5,-2). We will now substitute this these values into the formula. The length of the line is 10.3 to 3 significant figures.

## Parallel & Perpendicular Lines

Now that you posses some advanced coordinate geometry skills, you should have a look at the equations of parallel  and perpendicular lines. Please share this page if you like it or found it helpful!
(-1,-1)
(0,2)
(6,3)
(-6,-3)
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