In what ration does $X = Y$ divide the line segment joining points $A (4, 8)$ and $B (2, - 9)$

11 : 2

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4 : 9

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4 : 11

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None

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Solution

The correct option is C $4 : 11$
$X = Y$ Let required ration $k : 1$
$X = \frac{k (2) + 1 (4)}{k + 1} = Y = \frac{k (- 9) + 1 (8)}{k + 1}$
$2 k + 4 = - 9 k + 8$
$11 k = 4, k = \frac{4}{11}$
Required ratio $k : 1$
or $\frac{4}{11} : 1$ or $4 : 11$

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