If A, B, C, are collinear?

If A, B, C, are collinear, write an equation that can be used to find the value of k





A(1,1)


B(3,2)


C(k,4)





express the slope of BC in terms of k

If A, B, C, are collinear?
If A, B and C are colinear they lie on a straight line. That means that the gradient from A to B is the same as from B to C:





therefore





yB - yA yC - yB


------------ = ----------


xB - xA xC - xB





2-1 4-2


---- = ------


3 -1 k - 3





1 2


-- = ---


2 k-3


k-3 = 4


k=7