Question

If the points A(1,2) ,O(0,0), C(a,b) are collinear then find ratio a is to b.

Please give the answer based on those three methods of co-ordinate geometry and not on slope and alll

Answer 1

if points A, B and C are collinear ,

then area(tri ABC) = 0

1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)] = 0

1/2[1(0-b) + 0(b-2) + a(2-0)] = 0

1/2(-b + 0 + 2a) = 0

2a-b = 0

2a=b

a/b=1/2

hope this helps