 Okay, we just recreated the coordinate system that we've had on the other wall, and from this we already figured out what the slope was, which is y2 minus y2 minus y1 divided by x2 minus x1. And then we figured out what the midpoint was, which was here, which was taking the average of the x's and the average of the y's. The third most important thing they ask you to do with lines is to figure out what the distance between these two lines is. Now the distance between these two lines comes out through the, is derived from the Pythagorean Theorem. Now the Pythagorean Theorem, if you remember, is a right triangle. So all we're doing is, for this line, is taking the points and connecting up the y's and connecting up the x's and making vertical and horizontal lines. And that way these guys become right angles. Now the way you do the Pythagorean Theorem, you have a, b, and you've got side c. So according to the Pythagorean Theorem, the formula is a squared plus b squared is equal to c squared. Now that's our a, so what we have to figure out is what the distance is from here to here. The distance from here to here is just the x's subtracted from each other. So the formula for the distance becomes x2 minus x1. That's the distance for the x's. Now x2, you can choose either one to be x2 and either one to be x1, it doesn't make a difference because the value stays the same. So let's choose negative 5 as our x2. So this becomes negative 5 minus 2 gives us negative 7. Now when you're trying to figure out distance, you don't deal with the negative numbers. So the distance from here to here is not negative 7, it's really 7. So what you do is you take the absolute value of this. Now we'll talk about this absolute value just means no matter what this number is it comes out positive. So this becomes 7. So x2 minus x1 is really just 7. Then you do it for the y's as well. Y's, we chose this one to be our x2, x2. So we're going to choose this to be our y2. So y2, the formula for figuring out the distance, the vertical distance is going to be y2 minus y1. So y2 is 2 minus negative 3. Now as we talked about before, a negative number subtracted because positive, because 2 negatives make a positive. So this becomes 5. So the distance from here to here is 5. Now if we go to our formula, the Pythagorean theorem is this. Now the symbol that they use for distance between a line, two points, or the distance for a line between two points is d. So the way you can rewrite the Pythagorean theorem is d squared is equal to a squared, which is really x2 minus x1 squared. So this becomes bracket x2 minus x1 squared plus y2 minus y1 squared, which is the vertical distance. y2 minus y1 in brackets, the whole thing squared. Now you really don't want distance. You want distance squared. So what you do is, the formula that you should remember, sometimes they get you on test, but later on when you go to math 11 or 12, they're not going to give it to you. You have to know this formula is distance is equal to the square root of all that, which is x2 minus x1 squared plus y2 minus y1 squared. That's the distance formula. And we figured out what x2 minus x1 was, which was negative 5 minus 2. So this becomes, I'm just going to recreate it here so you see how it follows. It becomes negative 5 minus 2 squared plus y2 was 2, y1 was negative 3. So 2 minus negative 3 squared. Negative 5 minus 2 is negative 7. Negative 7 plus negative and negative becomes positive 5 squared. Now negative 7 squared, I just stated this that you can't have a negative distance, but it doesn't really make a difference because when you square it, it becomes positive. And negative times the negative is positive. So negative 7 squared is 49 plus 5 squared is 25. So the distance is the square root. When you add these, 49 plus 25, 5 plus 9 is 14. You carry the one out. 2 plus 4 is 6 plus 1 is 7. So 74. So square root of 74. So the distance between these two points is the square root of 74. Now that's not a perfect square. So all you do is you use your calculator to figure out what that number is. So the distance from here to here, let's stick with orange, is the square root of 74. And that's how you figure out the three most important things with lines. The slope, the midpoint, and the distance. From there, we can go on to equation of a line. Good luck.