Question

The points (K,1), (5,2), and (8,3) lie on a straight line. Find the value of K.

Answer 1

colinear...that means AB + BC = AC

that means...find the distance between (K,1) and (5,2)

then find the distance between (5,2) and (8,3)

add those distances

the sum must be equal to the distance from (K,1) to (8,3)

do you get what im pointing out?

Answer 2

that is the traditional way of solving it...but maybe you can just use slopes...just maybe

Answer 3

how du yu find the distances?

Answer 4

use slope
k wud be 2

Answer 5

So with slopes:\[m= \frac{3-2}{8-5} = \frac{1}{3}\]
And now:
\[\frac{1}{3}=\frac{2-1}{5-k} => 3 = 5-k => k=2\]