Use the distance formula to determine whether the points lie on the same line.

Question

(0,4),(7,-6),(-5,11).
I know the distance formula, but I don't see how that will help me find out if they lie on the same line.

Answer 1

distance between (0,4) and (7,-6) = √(49+100) = √149
distance between (7,-6) and (-5,11) = √(144+289) = √433
distance between (0,4) and (-5,11) = √(25+49) = √74

if they are collinear, then
√74 + √149 = √433
IS it ??

√74 + √149 = 20.80888088
√433 = 20.80865205
difference is .000228

had you simply graphed it, you would not have noticed the difference, but there is a difference, so the points are NOT collinear.

check: slope of 1st segment = -10/7
slope of another segment = 7/-5

since -10/7 ≠ -7/5 , they are not collinear.
(notice the slopes are close)
-1.42857 vs -1.4 , angles are 55.0° vs 54.5°