00:01
So for this problem, we want to find the area of the triangle with our three points as the vertices of our triangle.
00:07
And so we're given the formula for finding the area of a triangle using two adjacent sides.
00:13
And since our shape is a triangle, we know that any two sides that we choose are going to be adjacent.
00:19
So i'm going to label my points, a, b, and c.
00:23
So first i'm going to calculate vector a, b, which is going to be given to us by our terminal point of b minus our initial point.
00:30
Of a.
00:31
So that's negative 2 minus 2, which will be negative 4.
00:35
Negative 4 minus 4, which is negative 8, and finally 0 minus 0, which is 0.
00:41
And for my second side that i'm going to use, i want to calculate vector b .c.
00:47
So again, this is going to be c minus b.
00:49
So 0 minus negative 2 will be positive 2.
00:52
0 minus negative 4 will be positive 4.
00:56
And finally, 4 minus 0 is 4.
00:58
So from here, using our formula, i know i want to find first the cross product of our two vectors.
01:06
So to calculate the cross product of vector a, b, and vector b, c, i'm going to use the method of determinants with co -factor expansion.
01:15
So our first row comes from our three unit vectors, i, j, and k.
01:19
Our second row is going to be the first vector in our cross product.
01:24
So that's vector a, b, which we said is negative 4, negative 8, 0 .0 .0...