Question

P is a point on the line segment AB dividing it in the ratio 2 : 3. If the coordinates of A and Bare (-2,3) and (8,8), find if Plies on the line 7x - 2y =4.

Answer 1

Let the point P on the line segment AB be P( a,b)

Also, given that P( a,b) divides the line segment AB in the ratio 2 : 3

i.e. AP: PB = 2: 3

Coordinates of Pare,

P (a,b) = P `((16 - 6)/5 , (16 + 9)/5)` = P(2,5)

If P (a,b) lies on the line 7 x -2y = 4, then will satisfy the equation of the line 

LHS 7(2) - 2(5) = 14 - 10 = 4 = RHS

Yes, the [oint P (2,5) lies on the line 7x - 2y = 4