Friday, December 30, 2016

College Algebra, Chapter 2, 2.4, Section 2.4, Problem 60

Use slopes to determine whether the given points are collinear.

a.) (1,1),(3,9),(6,21)

b.) (1,3),(1,7),(4,15)

a.) Let m1 be the slope through points (1,1) and (3,9), m2 be the slope through points (1,1) and (6,21), m3 be the slope through (3,9) and (6,21).


m1=9131=82=4m2=21161=205=4m3=21963=123=4


Since m1=m2=m3, all the points are collinear.

b.) Similarly, let m1 be the slope through (1,3) and (1,7)

m2 be the slope through (1,7) and (4,15)

m3 be the slope through (1,3) and (4,15)


m1=731(1)=42=2m2=15741=83m3=1534(1)=125


Since m1m2m3, the points do not lie on the same line.

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