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=9−13−1=82=4m2=21−16−1=205=4m3=21−96−3=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=7−31−(−1)=42=2m2=15−74−1=83m3=15−34−(−1)=125
Since m1≠m2≠m3, the points do not lie on the same line.
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