This past week I reviewed graphing basics and how to find the distance between two points. Let's start with some graphing basics. Points on a graph are denoted (x,y) where x is the distance a point is from the origin (0,0) on the x or horizontal axis and y is the distance from the origin on the y or vertical axis. A graph has 4 quadrants. Points in quadrant 1 will have both a positive x and y value so (x,y). Points in quadrant 2 will have a negative x and positive y (-x,y). In quadrant 3 both the x and y values are negative (-x,-y) and in quadrant 4 the y value is negative while the x value is positive (x,-y). It is important to note that while a graph will not show all the numbers the x and y axis extend indefinitely in both the negative and positive directions.
We can find the distance between two points using the Pythagorean Theorem a squared plus b squared = c squared where c is the hypotenuse of a right triangle. No matter which two points we look at they all can be looked at as being a part of a right triangle. So if we were going to find the distance between the point (1,2) and (2,4) we need to look at the big picture. The distance between the two x coordinates 1 and 2 is one and the distance between the two y coordinates 2 and 4 is 2. 1 squared is 1 and 2 squared is 4, one plus 4 is 5. Then we take the square root of 5 to get the distance between those two points. So the distance formula is