# Week 11 – Finding Distances on a Coordinate Plane

Before we start to find the distances of lines, there are three different types of lines that you can find. The first one is a horizontal line, a horizontal line is a line that is a straight line that goes from left to right. And on a coordinate plane, a horizontal line runs parallel to the x-axis. The next one is a vertical line that is a straight line that goes up and down. On a coordinate plane, a vertical line will run parallel to the y-axis. The final type of line is an oblique line. It is lines that are drawn at an angle (other than 900) to the horizon. They are neither vertical nor horizontal.

There are two ways to find different types of distances on a coordinate plane. If the coordinate plane you are using has small or easy numbers to count and the line is either horizontal or vertical you can count the points to find the distances between the two points. However, as it gets harder when the numbers get bigger or the line is an oblique line, you need to use another method.

When the line is either horizontal or vertical the way to find the distances is to take the coordinates of the to points that you want to find the distances between. Then the points that are different (the x-axis ones for horizontal lines, and the y-axis ones for the vertical lines) and subtract them. Make sure that the number you get is positive and if it is not, just change it to be positive.

However, is the line is oblique, there is another method to find the distances of the points. When you look at this line on a coordinate plane it looks like a hypotenuse line which gives you a big clue on how to solve for the distance. You can make a triangle and find the distances of the vertical and horizontal line of the triangle. Finally, you can use Pythagoras’s theory ( a squared + b squared = c squared) to find the distances of the last line.

Some examples: 