SOLUTION: show that the pionts A(1,-1), B(4,-2) and C(16,1) are collinear

Algebra ->  Linear-equations -> SOLUTION: show that the pionts A(1,-1), B(4,-2) and C(16,1) are collinear      Log On


   



Question 741263: show that the pionts A(1,-1), B(4,-2) and C(16,1) are collinear
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if the points A(1,-1), B(4,-2) and C(16,1) are collinear, they will lie in a straight line;

in order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope}}}
Hence it will be sufficient to prove that the slope calculated taking 2+ points at a time should be equal.

Slope of line taking points (x1,y1)= (1,-1) and (x2,y2)=(4,-2) is
slope=%28y2-y1%29%2F%28x2-x1%29
slope=%28-2-%28-1%29%29%2F%284-1%29
slope=%28-2%2B1%29%2F3
slope=-1%2F3
slope=-0.333

Slope of line taking points (x1,y1)= (1,-1) and (x2,y2)=(16,1) is
slope=%28y2-y1%29%2F%28x2-x1%29
slope=%281-%28-1%29%29%2F%2816-1%29
slope=%281%2B1%29%2F15
slope=2%2F15
slope=0.133
since -0.333%3C%3E0.133, given points are NOT collinear