Question

Find the sum of ratio in which P (4,m) divided the line segment joining the points A(2,3)and B (6,-3) hence find 'm'

Answer 1

Hey friend, Harish here.

Here is your answer:

Given that,

A line segment with two points A(2,3) & B(6,-3)

To Find,

Sum of ratios in which the points divide the line, And the value of P.

Solution:

Let the line be,
                                                     P( 4, m)

               A( 2 , 3)._______________|_______________.B(6 , -3)


& Let P Divide the line in the ration K: 1.


Then By using section formula , We get,

⇒  $\frac{(6\times k) + 2}{(k+1)} = 4$

⇒  $6k + 2 = 4(k+1)$

⇒  $6k + 2 = 4k+4$

⇒  $6k - 4k = 4-2$

⇒  $2k = 2$

⇒  $k=1$
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

We know that,

⇒  $\frac{(k\times (-3)) + 3}{k+1}= m$

⇒  $\frac{(1\times (-3))+3}{1+1 } =m$

⇒  $m = \frac{-3 + 3 }{2} = \frac{0}{2} = 0$

Therefore P(4,m) divides AB in the ratio 1:1.

And m is equal to 0.
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Hope my answer is helpful to you.