in this video we're going to talk about how to use the distance formula to calculate the distance between two points so let's say if we have two points point a and point b the coordinates of point a our one two and the coordinates of point b are nine comma seventeen use the distance formula to calculate the distance between those two points so here's the formula that you need it's equal to the square root of x2 minus x1 squared plus y2 minus y1 squared so you need to know what is x1 and what is x2 so x is the first point y is the second one so this is x1 that's y1 and we can call this x2 and y2 so we can see that x2 is nine x1 is one y2 is 17 and y1 is two so nine minus one is eight and seventeen minus two is fifteen now eight squared eight times eight that's 64 and 15 squared is 225 now we need to add 64 and 225 so that's 289 and the square root of 289 is 17. so this is the distance between these two points it's 17 units apart now for the sake of practice let's try another example so let's say that c has the coordinates 5 negative 16 and d has the coordinates negative 2 comma 8. so go ahead and use the distance formula to calculate the distance between points c and d so we're going to call this x1 y1 this is going to be x2 and y2 so d is equal to the square root of x two minus x one squared plus y two minus y one squared so x two in this example is negative two minus x one which is positive five now y two is eight minus y one which is negative sixteen negative two minus five is negative seven and eight minus negative sixteen because we have two negative signs we can make it positive a negative times a negative is a positive number so 8 plus 16 is 24 and so this is what we now have negative 7 squared which is negative 7 times negative 7 that's positive 49. 24 times 24 is 576 and 576 plus 49 is 625 so now we need to take the square root of 625 and that's equal to 25. so the distance between point c and d is 25 units long number three calculate the area of a circle with center two comma one and point p six comma four so let's start with a graph so this is six and this is four so point p is located here at six comma four x is six and y is four and the center is at two comma one so the center of the circle is right there so we can draw a circle around the center it's probably gonna look something like this and that's a rough sketch now the distance between the center and some point on a circle is the radius so what we need to do is use a distance formula to calculate the distance between the center of the circle and some point p which is on a circle and if we could find that that will give us the radius and then we can use that to calculate the area the area of the circle is pi r squared so let's call this x and y1 and 6 is going to be x2 4 is y2 so let's start with the formula d is equal to the square root of x2 minus x1 squared plus y2 minus y1 squared so in this example x2 is 6 x1 is 2. y two is four y one is one now six minus two is four and four minus one is three four times four is 16 3 squared is 9 and 16 plus 9 is 25 and the square root of 25 is 5. so the radius of the circle is 5 units long so now we can calculate the area so it's pi r squared that's going to be pi times 5 squared 5 squared is 25 so the answer is 25 pi square units so that's the area of the circle which is basically the area of the shader region you