Identify the ratio in which the line joining (4,5) and (-10,2) is cut by the Y - axis.

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Solution

The correct option is D

Refer to fig., $tan θ$ = $(\frac{y - 2}{10}) = (\frac{5 - y}{4})$
4y - 8 = 50 - 10y
14y = 58
y = $\frac{29}{7}$
also, using Pythagoras theorem, we have,
$a^{2} = (10^{2} + (y - 2)^{2}) = \frac{5125}{49}$
$b^{2} = (4^{2} + (5 - y)^{2}) = \frac{820}{49}$
hence, the line gets divided in the ratio $2 : 5$

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Similar questions

In what ratio is the line joining the points:

(2, -3) & (5, 6) divided by the – axis.

(3, 4) & (-2, 1) divided by the y – axis.

If the line $2 x + y = k$ passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2 then k equals:

(- 2, 5)

(- 5, - 6)

y = - 3

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