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Section Formula

In what ratio...

Question

In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis ?

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Solution

Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1.

$y equals fraction numerator k y subscript 2 plus y subscript 1 over denominator k plus 1 end fraction 0 equals fraction numerator k cross times 6 plus 1 cross times left parenthesis negative 3 right parenthesis over denominator k plus 1 end fraction 0 equals 6 k minus 3 k equals 1 half$

Thus, the required ratio is 1: 2.

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