Question

The point on x-axis which divides the line segment joining (2, 3) and
(6,- 9) in the ratio 1:3 is
(A) (4, -3)
(B) (6,0)
(C) (3,0)
(D) (0,3)​

Answer 1

Answer:

(c) 3,0

Step-by-step explanation:

using section formula

(x,y)=(1×6+3×6/1+3,1×-9+3×3/1+3)

=(6+6/4,-9+9/4)

=(12/4,0/4)

=(3,0)

Answer 2

The correct answer is the option C) (3,0) i.e the line segment is divided by the point (3,0) in the ratio 1:3.

Let the point that divides the line joining points (2,3) and (6,-9) in the ratio 1:3 be equal to (x,y) .

Using the section formula to find the coordinates of the point -

x = (m1x2 + m2x1)/(m1+m2)

y = (m1y2 + m2y1)/(m1+m2)

m1 = 1 , m2 = 3 , x1 = 2 , x2 = 6 , y1 = 3 , y2 = -9

x = (1×6 + 3×2)/4 = 3

y = (1×-9 + 3×3)/4 = 0

The coordinates of the point on the x-axis is (3,0).