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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Answer: Option A
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Concept: 1 Mark
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Answer: 1 Mark
Let the required ratio be λ:1. Then, the coordinates of the point of division are,
R(5λ+2λ+1,6λ−3λ+1)
But, it is a point on x-axis on which y-coordinates of every point is zero.
∴6λ−3λ+1=0⇒λ=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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