# In what ratio is the line joining A(0, 3) and B (4, -1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis - Mathematics

Sum

In what ratio is the line joining A(0, 3) and B (4, -1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis

#### Solution

Let the line segment AB intersects the x-axis by point P (x, 0) in the ratio k: 1.

therefore (x,0)=((kxx4+1xx0)/(k+1),(kxx(-1)+1xx3)/(k+1))

therefore (x,0)=((4k)/(k+1),(-k+3)/(k+1))

=>0=(-k+3)/(k+1)

=>k=3

Thus, the required ratio in which P divides AB is 3: 1.

Also, we have:

x=(4k)/(k+1)

=>x=(4xx3)/(3+1)=12/4=3

Thus, the co-ordinates of point P are (3, 0).

Concept: Section Formula
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (C) | Q 6 | Page 183