# Math Help - determinants

1. ## determinants

how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
lx1,y1,1l
lx2,y2,1l
lx3,y3,1l is 0.

the above is a 3x3 matrix.

2. Originally Posted by alexandrabel90
how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
lx1,y1,1l
lx2,y2,1l
lx3,y3,1l is 0.

the above is a 3x3 matrix.
.

3. sorry, i cant seem to see what you have typed:/

4. The area of the triangle formed by the three given point is half of the absolute value of determinant.
Thus if the three points are colinear, then the determinant is equal to 0.

5. what does it mean that the area formed by the 3 given pts is half the absolute value of the determinant?

could you explain further?
thank you!

6. This is the formulla to find the area of a triangle formed by three points whose coordinates are given.