Question

3
29. Find the ratio in which the line segment joining the points
(-3, 10) and (6, –8) is divided by (-1, 6)
(-1, 6) বিন্দুটোৱে (-3, 10) আৰু (6, –8)বিন্দু সংযােগী ৰেখাক কি
অনুপাতত ভাগ কৰিব ?​

Answer 1

Solution :-

Let the points (-3, 10), (6, –8) and (-1, 6) be A, B and C respectively.

Let the ratio be k: 1.

So,

$x = -1 , \:y = 6\\\\x_{1} = -3 , \:y_{1} = 10\\\\x_{2} = 6 , \:y_{2} = -8\\\\m_{1} = k , \:m_{2} = 1$

By the median Formula,

=> (x,y) = $(\frac{m_{1}\times x_{2} +m_{2}\times x_{1} }{m_{1} +m_{2}} ,\frac{m_{1}\times y_{2} +m_{2}\times y_{1} }{m_{1} +m_{2}})$

=> (-1, 6) = $(\frac{k\times 6 +1\times -3}{k+1}} ,\frac{k\times -8 +1\times 10 }{k+1})$

Solving it, using the x-coordinate

=> -1 = $\frac{k\times 6 +1\times -3}{k+1}$

=> -1 = $\frac{6k -3}{k+1}$

=> -1(k+1) = 6k -3

=> -k -1 = 6k - 3

=> -1 + 3 = 6k +k

=> 2 = 7k

=> $\frac{2}{7}$ = k

The ratio is k:1.

= $\frac{2}{7}$ : 1

=  $\frac{2}{7}$

So, the ratio in which the line segment joining the points

(-3, 10) and (6, –8) is divided by (-1, 6) is $\frac{2}{7}$ .