Geo2.15

Show that the points $(-5,1),(5,5),(10,7)\,$ are collinear.

Equation of the line joining the first two points is

$y-1=\frac{5-1}{5+5}(x+5)\,$

$y-1=\frac{2}{5}(x+5)\,$

$5y-5=2x+10\,$

$2x-5y+15=0\,$

Now if we prove that the third point lies on this equation, then the three points are collinear.

$2(10)-5(7)+15=-15+15=0\,$

Hence the three points are collinear.