Question:
if the points [x,y] is collinear with the points [a,0] and [0,b], then prove that x/a + y/b = 1.
Answer:
Let the points are A(x, y), B(a, 0) and C(0, b).
If the points A, B, C are collinear, then the area of the triangle will be equal to zero
=> (1/2)*{x(0 - b) + a(b - y) + 0(y - 0)} = 0
=> -bx + ab - ay = 0
=> bx + ay = ab
=> bx/ab + ay/ab = 1
=> x/a + y/b = 1
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