00:01
So in this problem, you're given the corner or the vertices for a triangle.
00:04
So you have a, which is the ordered pair negative 1, negative 2.
00:07
B would be at the ordered pair 6, 2.
00:09
And c is at the ordered pair 4, 6.
00:11
And we're told again that they form a triangle.
00:13
So the first thing you're being asked to do is to find the midpoint of a, b.
00:17
So midpoint of a to b.
00:23
Well, we have a formula to find the midpoint.
00:25
So this midpoint, they want us to call m.
00:27
What we do is we take the average of the x -coordinates.
00:29
So we do x sub 1 plus x sub 2 divided by 2.
00:32
That gives us the x -coordinate for the midpoint.
00:34
And similarly, to find the y -coordinate, we find the average of the y -coordinates.
00:38
So y sub 1 plus y sub 2 divided by 2.
00:41
So let's go ahead and substitute in our values.
00:43
So x sub 1 would be the x -coordinate of a, so negative 1, plus x sub 2, which is the x -coordinate of b, which is 6.
00:50
We'll divide that by 2.
00:51
For y, we'll take the y -coordinate of a, which is negative 2, and add it to the x or y -coordinate of b, which is positive 2.
00:59
And now we'll go ahead and simplify.
01:01
So m, for x -coordinate, we have negative 1 plus 6, which is 5.
01:05
So we have 5 halves.
01:07
And negative 2 plus 2 is equal to 0.
01:09
So that'd be 0 over 2.
01:11
Well, 5 divided by 2 is equal to 2 .5.
01:14
And 0 divided by 2 is 0.
01:16
So now we have the coordinate of our midpoint.
01:18
It'd be 2 .50.
01:21
Now, in part b, we want to show that...
01:24
Oh, i'm sorry.
01:27
We want to find the midpoint of ab and the midpoint of ac.
01:30
Okay, so we're going to also find the midpoint of a to c.
01:33
So again, for the x -coordinate, we're going to take the x -coordinate of a, which is negative 1, and we're going to add it to the x -coordinate of c, which is 4, divided by 2.
01:42
And for the y -coordinate, we'll take the y -coordinate of a, which is negative 2, add it to the y -coordinate of c, which is 6, and we'll divide that by 2.
01:52
So now let's go ahead and simplify.
01:54
So negative 1 plus 4 is 3, so 3 over 2.
01:57
For y, negative 2 plus 6 is 4, so we have 4 over 2.
02:01
Then we have 3 divided by 2, which is 1 .5.
02:04
And 4 divided by 2 is 2.
02:06
So now we have the coordinates for b...
02:09
Or sorry, for n and m.
02:11
Now we can go ahead and take a look at part b.
02:14
We want to prove that mn is parallel to bc.
02:17
Well, if you recall, two lines would be parallel if they have the same slope.
02:21
So now we just have to find the slope for each of these segments.
02:24
So let's start with mn.
02:26
So remember, to find the slope, what we're going to do is we're going to find the change in the y -coordinates, y sub 2 minus y sub 1, and divide it by the change in the x -coordinates, x sub 2 minus x sub 1.
02:37
So for m, if you scroll up a little bit, the y -coordinate was 0, so 0 minus, and n is 2.
02:44
For the denominator, the x -coordinate for m was 2 .5.
02:48
So let's see if i can...
02:50
2 .5.
02:52
Looks like i'm getting pretty low to the bottom there...