00:04
We are given two points in the cartesian plane, and in part a, we are asked to plot these points.
00:15
So the points are 6, negative 3, and 6 .5.
00:20
So to plot these points, notice that the x coordinates of the points are both 6, and the y coordinates range from negative 3 to 5.
00:30
So i'll just draw the x, y, plane, or the x, axis will range from, let's say, 0 to 6 and the y axis will range from negative 5 to positive 5.
01:13
Now our first point 6 negative 3 is located about here and our second point 6 5 is located about here at the intersection of the lines x equals 6 and y equals 5.
01:35
Notice that both of these points lie on the line, x equals 6.
01:44
Then, in part b, we're asked to find the distance between these two points.
01:54
So from the picture, it seems intuitive to think the distance is just going to be 5 plus 3, which is 8, right? let's check this with our distance formula.
02:06
So the distance between these two points, 6 -9 -3, and 6, 5.
02:19
Our distance formula, this is the square root of 6 minus 6 squared plus negative 3 minus 5 squared, which is equal to the square root of 0 squared, which is 0, plus negative 8 squared, which is 64, or the square root of 64, which is 8.
02:51
Because distance is always positive, we're taking the positive square root.
02:57
So just as we predicted, the distance is 8...