Posted by Christina on Friday, September 16, 2011 at 11:44am.
Use the distance formula to determine whether the points lie on the same line.
(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.

Math  Reiny, Friday, September 16, 2011 at 12:51pm
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°