Question

L is a point on the line segment PQ dividing it in the ratio 1 : 3. If the coordinates of P and Q are (3, 7) and ( 11,-5) respectively, find if L lies on the line 2x + 5y = 20.

Answer 1

Let L(a,b) be the point on line segment PQ dividing it in the ratio 1 : 3

i.e. PL : LQ = 1 : 3

Coordinates of L are,

L (a,b) = L `((11 + 9)/4 , (-5 + 21)/4)`

= L (5,4)

If L(a,b) lies on the line 2x + 5y = 20, then it wll satisfy the equation of the line

LHS = 2 (5) + 5 (4) = 10 + 20 = 30 ≠ RHS
No, L (a,b) does not lie on the line 2x + 5y = 20