Question

If the points (a,0) (0,b) and (3,4) are collinear ,S.T 3/a+4/b=1

Answer 1

If the points (a, 0) , (0, b) and (3, 4) are collinear.

we have to show that 3/a + 4/b = 1.

proof : if three points are collinear, it means three points lie on the same line.

therefore, area of triangle formed by three points must be zero.

here points (a, 0) , (0, b) and (3, 4) are collinear.

so, area of triangle formed by (a,0) , (0, b) and (3,4) = 0

⇒1/2 [a(b - 4) + 0(4 - 0) + 3(0 - b)] = 0

⇒a(b - 4) + 3(-b) = 0

⇒ab - 4a - 3b = 0

⇒ab = 4a + 3b

⇒ab/ab = 4a/ab + 3b/ab

⇒1 = 4/b + 3/a

⇒3/a + 4/b = 1 hence proved.