00:01
Given p at three squared a two comma four square to five and q at square to two comma negative squares of five we're going to find the distance between p and q as well as the midpoint m of the line segment so the distance formula so d of p q is the square root of x2 minus x1 squared plus y2 minus y1 squared.
00:28
So the first thing i'm going to do here is i'm going to label my points x1 y1 and x2 y2.
00:37
And now we can substitute those in.
00:39
So we get d pq equals the square root x2 is the square root of 2 minus x1, which is three square roots of two squared plus y2 is this negative square root of 5 minus y1.
00:56
Is four square roots of five squared.
01:04
We get two minus three square to two, which is negative two squared to two squared plus negative square of five minus four squirts of five is negative five squared squared.
01:23
From there, we get the distance of pq equals the square root of four times two because negative two squared is negative two times two, which is four, the square to two squared is two, plus negative 5 squared is 25 times the square of 5 squared is 5.
01:51
4 times 2 is 8, and 25 times 5 is 125.
01:57
So we get the distance of pq is a square root of 8 plus 125, which is 133.
02:08
And if we want to round that, we could round that to two decimal places if we want...