The ratio in which the point (-4,6) internally divides the line segment joining (-6,10) and (3,-8) is

5:2

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2:7

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2:9

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Solution

The correct option is B 2:7
Let the required ratio be $m : n$

Coordinates of end points are (-6,10) and (3,-8).
Coordinates of the point dividing the line segment is (-4,6)

Thus, $- 4 = \frac{m \times (3) + n \times (- 6)}{m + n}$
$\Rightarrow - 4 m - 4 n = 3 m - 6 n$
$\Rightarrow 2 n = 7 m$
$\Rightarrow \frac{m}{n} = \frac{2}{7}$

Thus, the required ratio is 2:7.

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The ratio in which the point (-4,6) internally divides the line segment joining (-6,10) and (3,-8) is

The correct option is B 2:7Let the required ratio be m:n Coordinates of end points are (-6,10) and (3,-8). Coordinates of the point dividing the line segment is (-4,6) Thus,−4=m×(3)+n×(−6)m+n ⇒−4m−4n=3m−6n ⇒2n=7m ⇒mn=27 Thus, the required ratio is 2:7.