Are the set of points C(1, -1), D(3, 4), E(5, 8) are collinear?

1 Answer
George C.
Jun 20, 2015

No - the slope of a line through #(1, -1)# and #(3, 4)# is #5/2# while the slope of a line through #(3, 4)# and #(5, 8)# is #2#, so there is no one straight line that passes through all three.

Explanation:

If a line passes through #(x_1, y_1)# and #(x_2, y_2)# then its slope m is given by the formula:

#m = (Delta y) / (Delta x) = (y_2 - y_1) / (x_2 - x_1)#

So a line through #(1, -1)# and #(3, 4)# has slope:

#(4 - (-1))/(3-1) = 5/2#

and a line through #(3, 4)# and #(5, 8)# has slope:

#(8-4)/(5-3) = 4/2 = 2#

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