For week 14 of Math 10, we are expanding more on linear equations and now finding the distance between two points in a graph. For this weeks blog post, I will be explaining how to find the distance between two points.
For this example, we are going to use points with the coordinates of (6, 6) and (9, -2). Now if these points where on the same grid line either horizontally or vertically then you could just subtract the two numbers to find the difference. However, we are trying to find the distance of the diagonal line the encompasses the two coordinates. As you can see, we cannot count the boxes or subtract numbers because they two points are not on the same axis so counting squares is not an option. Instead, we can use a method that we have used a lot this year which is Pythagoras or the Pythagorean theorem. To do this we need to create triangle out of the line segment where the two other lines travel along the lines. Now that we have a triangle, we can count how long the other sides are that are vertical or horizontal. We then can square them, add them together, and either square root it or leave it as a radical if it is not a perfect square. In this case we have 3 and 8 as the length of our sides. So first we need to square them so we end up with 9 and 64. Next we add them together to get 