we are building a road that links the points a = (12 ,21) and b =(17,23) another point is in c =(3,9) it is possible that a single road allows to join these three points?

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope ab

we have

a = (12 ,21) and b =(17,23)

substitute

$m=\frac{23-21}{17-12}$

$m=\frac{2}{5}$

step 2

Find the slope ac

we have

a = (12 ,21) and c =(3,9)

substitute

$m=\frac{9-21}{3-12}$

$m=\frac{-12}{-9}$

simplify

$m=\frac{4}{3}$

step 3

Compare slopes ab and ac

The slopes are different

That means ----> is not possible that a single road allows to join these three points

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