consider the points: a(-5,20), b(2,-1) and c(4,-7). show that a, b and c lie on the same straight line.

Question

consider the points:
a(-5,20), b(2,-1) and c(4,-7).

These points all lie on the same straight line if it can be shown that the gradient of AB is equal to the gradient BC.

show that a, b and c lie on the same straight line.

Answer 1

To find the gradient of AB, you find the slope:

m_AB = (-1-20)/(2--5) = -21/7

 

To find the gradient of BC, find the slope of BC:

 

m_BC = (-7-1)/(4-2) = -8/2 = -4

 

Based on this analysis, the points are not collinear. Did you mix up a negative sign somewhere?  However, this is how you would solve the problem - if the slopes are the same, then the points are collinear.