Learn about Distance Formula and Pythagorean Theorem Applications In this lesson let's learn how to do word problems when it comes to coordinate planes, distance Pythagorean Theorem, etcetera. The problems says that there are four bases on a baseball field of course and they form a square with each side being 90 feet. So this is the home base, this length from home base to the first base is 90 feet, first to second is 90 feet, second to third is 90 feet and third to fourth is 90 feet, okay. So this is a perfect square. When a player threw us a ball from the home plate to the second base what's the distance of the throw? So we need to find this distance of this diagonal, okay. So, what I've done is I basically drawn what a baseball diamond could look like as a square on a coordinate plane. This is the home plate, this is base one, base two, base three. And again as you see we started zero-zero this is about 90 feet, 90 units and then I went 90 units here. So I went from 90-0 to 90-90 again came back 90 units. Right, so we need to find this distance. I'm going to teach you two ways of doing it. The first is using the distance formula. Right, what have we learned that distance D is the square root of X2 – X1² + Y2 – Y1² right. So in this case the distance D, what is the X2 and X1 values, X2 is this one is 90, X1 is 0² + Y2 is also 90 - 0², Y2 is 90, Y1 is 0. Okay, so that distance D is 90² which is 8100 + 8100 = square root of 16,200. Now, the square root of 16,200 is the length of this particular line segment which is D it becomes 127.3 and what's the unit feet. Right, so that’s one way of doing it, which is finding it using the distance formula. The other way of doing it is using the Pythagorean Theorem. Okay, so let me create more space. This is a right angle triangle, right, and this one. Right this three points form a right angle triangle. So what is—if this is A and this is B and this is C, what we know is C equals square root of A² + B² right. So this length C is good enough what is A? well we know A is home base to first plate is 90², B is 90. So that’s the square root of 90² + 90² = 8100 + 8100 = 16,200, square root of 16,200 = 127.3, right. So again based on this, if this is 90 feet this is 90 feet, C is 127.3 feet and we have two different ways of getting out the same answer.