00:01
Okay, in this question we're finding an area of a figure given coordinates of vertices.
00:15
And this is a composite figure.
00:19
So let's draw a cartesian coordinate system.
00:27
And this is the x and this is the y.
00:31
We have a point at one comma four which is called a we have a point at four comma one which is called b we have a point at one comma one which is called b we have a point at one comma negative two which is called c and we have a point at negative three which is called d.
01:07
So the composite figure is this and we want to find the area.
01:18
So how do we do that? well let's divide it into two triangles.
01:31
Look a has a coordinate of one and c has a coordinate of one and c has a coordinate of one.
01:37
So we know this is a vertical line and d has a coordinate a y coordinate of one and b has a a y coordinate of one so this is a horizontal line.
01:54
So this is a right triangle.
01:58
This is a right triangle, this is a right triangle, this is a right triangle, this is a right triangle.
02:04
And we know the height of and width of each triangle.
02:11
We can actually just use our figure to determine the height and width of each triangle, and the area of a triangle is one half base times height.
02:24
So let's do that for each triangle, and it might just be the case that each triangle has the same area.
02:32
Well, we'll have to see.
02:37
I'm not quite sure based on this drawing, but it looks promising.
02:43
If i had graph paper, it might be easier to see.
02:47
Anyways, the base of this triangle looks like has one, two, three.
03:00
So this is a three by one, two, three.
03:07
3 by 3.
03:09
Okay, i'm just finding the links of all of these triangles.
03:15
Here's one unit, another unit, another unit.
03:19
So, ooh, look at that's also 3.
03:22
And this one might not be 3.
03:25
This is 1 to 0, 0 to negative 1, negative 1 to negative 2, negative 2 to negative 3.
03:36
So we went from 1 to negative 3.
03:40
To negative 3...