Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between
the points, and (c) find the midpoint of the line
segment joining the points.
in this problem, we're going to be looking at three different parts. The first part is we're gonna point Plot the points to 10 and 10 to both points are positive. So we're I ano on Lee going to be using a quadrant one graph. Our first set of points is to 10 where X is to our wise 10. Our second set of points is 10 to our existen are wise to. Now that we've got both points plotted, we're going to draw a line that connects them. There is your graph of the points to tea and an 10 to our next part we're gonna do is we're gonna find the distance between the two points. In order to find the distance between two sets of coordinates, we're gonna use the distance formula. The distance formula says D or distance equals the square root of our second X coordinate minus our first X coordinate squared, plus our second y coordinate minus our first y coordinate square. So for this particular problem, we're gonna put the X and Y coordinates in place of the X and Y in the distance formula, so D will equal the square rate for our second X, We're gonna use the coordinate tiene minus our first X, which is to and we will square that difference. Plus our second Why coordinate is too, my ass. Our first wife coordinate is 10 and we will square that difference. 10 minus two is eight. We will square that, plus to modesty in is negative A and I'm gonna put that in parentheses and we will square that eight square is 64 plus negative. Eight squared is also 64 and 64 plus 64 is square root of 1 28 So our distance is the square root of 1 28 or it is approximately 11 and 31 hundreds. Our final step in this problem is to find the midpoint between the two points. So the midpoint is that center. Coordinate on the lot to find the midpoint. We're going to use the formula ex first eggs, plus or second eggs, the valuable to and our second our first. Why plus or second, why divide about two? We'll work each of these separately to find the coordinates because we're trying to find an X coordinate, and I y coordinate. So let's start with her ex values. Our first X is too, plus our second exes tent, and we will divide that by two. And if our why coordinates our first, why is 10 plus our second? Why is too? And we will also divide that Marty. So two plus 10 is 12. Divide about two and tam plus two is 12. The valley about two. So for both of these are actually end up in the same number 12 divided by two is six. So our X coordinate its six and our why coordinate? It's also 12 divided by two. So it's six. So that means on my line my midpoint is six six, which is at this location right here, halfway between both points.