Determine whether the points A (1,0) B(3,-5) C (2,2) lie on a straight line.

Expert Answers
justaguide eNotes educator| Certified Educator

To determine if three points lie on a line, first use two of the points and determine the equation of the line joining them. Then check if the third point lies on this line.

It has to be determined if A(1,0) B(3,-5) and C(2,2) lie on a straight line. Take the points A (1,0) and B(3,-5) to determine the equation of the line that joins them. It is given by:

`(y - 0)/(x - 1) = ( -5 - 0)/(3 - 1)`

=> `y/(x - 1) = -5/2`

=> 2y = 5 - 5x

=> 5x + 2y - 5 = 0

Now test if C(2, 2) lies on the line

5*2 + 2*2 - 5 = 10 - 4 - 5 = 1

This shows that C does not lie on the same line as A and B.

The three points do not lie on a straight line.