Question

Using determinant show that the points (1,0) (0,2) and (1,0) lie on a straight line.

Answer 1

The line joining (1,0) and (0,2) has a slope (2-0)/(0-1)=-2. The line joining (0,2) and (1,0) has a slope (0-2)/(1-0)=-2. So these points are colinear because (0,2) is a common point and the lines have the same slope.

The determinant is:

| 1 0 1 |

| 0 2 1 | = 1(2-0)-0+1(0-2)=2-2=0 which confirms collinearity.

| 1 0 1 |