Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. Hello. We're going to look at Cartesian coordinate systems. Cartesian coordinate system is made-up of a horizontal line and a vertical line. The horizontal line is called the X axis and it tells us how far right or left to go. The vertical line is called the Y axis, and it's going to tell us how far up or down to go. The two lines intersected a point. The point is referred to as the origin, and because we haven't gone left or right any, it's going to be coordinate zero and we haven't gone up or down any, it's going to also be zero. So the first coordinate is going to be our X, the 2nd is going to be our Y. The 1st is referred to as the abscissa and the 2nd is the ordinate. The abscissa once again tells us left or right and the ordinate tells us up or down. Now these two lines divide the graph into four sections. The four sections are referred to as quadrants and the quadrants get counted as the upper right going counterclockwise. So quadrant 1, quadrant 2, quadrant 3, and quadrant 4. We're going to look at the distance formula, which is based on two given points. Let's put a point here and call it X2Y2. And let's put another point maybe down here and call it X1Y1. Now the distance formula is really, really established off of a right triangle using the Pythagorean theorem. If we look at this right triangle and we want the distance of this line here, we can find it by using our concept of a ^2 + b ^2 = C ^2. The distance here is really found by just taking the farthest to the right point and subtracting the furthest to the left. Because it's a horizontal line, we just talk about the furthest right minus the furthest left X 2 -, X one. I'm going to do the same thing here. The highest coordinate minus the lowest. And because it's a vertical line, we're just going to look at the YSY 2 -, y one. So if we look at this, we'd get our A value as X2 minus X1 squared and our B value as Y 2 -, y one squared equaling Rd. squared. Well, how do we get rid of a square? We square root it and this is where the distance formula originates from, or one way to find the distance formula. Another important formula for us this semester is going to be the midpoint formula. And the midpoint formula states that if I know two points, the midpoint is the average of the X's. We take the 2X values, divide by two, and the two Y values added together and divided by two. That's how we find our midpoint. Have a great day.