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Question

In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.
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Solution

Concept: 1 Mark
Application: 1 Mark
Answer: 1 Mark 

Let the required ratio be λ:1. Then, the coordinates of the point of division are,

R(5λ+2λ+1,6λ3λ+1)

But, it is a point on x-axis on which y-coordinates of every point is zero.

6λ3λ+1=0λ=12

Thus, the required ratio is 12:1 or 1:2.

Substituting λ=12 in the coordinates of R.

R(5λ+2λ+1,0)

R(52+212+1,0)

R(9232,0)

R(3,0)

the coordinates of R are (3, 0)

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