Question

Show that (a, 1), (b, 1) and (c, 1) are collinear points

Answer 1

(a, 1), (b, 1), (c, 1)

the slope between any two of these

points is m = 0

m_ab = (1-1)/(b-a) = 0

m_ac = (1-1)/(c-a) = 0

m_bc = (1-1)/(c-b) = 0

This is a horizontal line. So long as

a, b, c are not equal ...

If a=b then (a, 1), (b, 1) are the same pont

If a=c then (a, 1), (c, 1) are the same point

If b=c then (b, 1), (c, 1) are the same point

If a=b=c then all three are actually the same point.

From the origin we go left or right a units and up 1

From the origin we go left or right b units and up 1

From the origin we go left or right c inits and up 1

Any two points with the same y value will

create a horizontal line of format y = c

where c is some number

In this case, (a, 1), (b, 1), (c, 1) are all on

the line y = 0x + 1 or y = 1