00:01
So for this problem, we are given three points that make up a triangle.
00:05
And to find the area of a triangle with our given sides, we know that the area is equal to one half of the magnitude of the cross product of two adjacent.
00:19
And so since we have a triangle, we know that any two sides that we pick will be adjacent.
00:23
So we can go ahead and find, if we label our points a, b, and c.
00:29
We can find a vector to represent a side a, b.
00:34
And so to do that, we know that we're going to subtract the initial point, point a, from the terminal point, which is point b.
00:41
So we'll get 2 minus 1, which is 1, 0 minus negative 4, which is positive 4, and 2 minus 3, which is negative 1.
00:50
And then we can go ahead and find side b, c, again, in vector form.
00:55
This time our vector will be negative 4, 2, negative 2.
01:01
And so from here we know that we need to find the cross product of our two vectors.
01:07
So we want to find a b cross vector b.
01:12
And so to set up our method of determinants with co -factor expansion, we know that our first row is going to be our three unit vectors, i, j and k.
01:21
Our second row will come from the first vector that we're finding in the cross product, which is 1 for negative 1.
01:28
And our third row is going to come from the second vector in our cross product, which will be negative 4 to negative 2...