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°

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