Question

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14

Answer 1

Let A(24/11,y) divides the line segment PQ in the ratio k:1.

Given P(2,-2) and Q(3,7).

Here x1 = 2, y1 = -2, x2= 3, y2 = 7, m = k,n = 1

We know that formula is:

$( \frac{mx2 + nx1}{m+n} , \frac{my2 + ny1}{m + n} )$

$( \frac{24}{11} ,y) = ( \frac{k * 3 + 1(2)}{k + 1} , \frac{k * 7 + 1(-2)}{k + 1} )$

$( \frac{24}{11},y) = (\frac{3k + 2}{k + 1} , \frac{7k-2}{k+1} )$

$\frac{24}{11} = \frac{3k + 2}{k + 1}$

3k + 22 = 24k + 24

9k = 2

k = 2/9

Therefore the ratio = 2:9.

Now,

$y = \frac{7k - 2}{k + 1}$

$y = \frac{7( \frac{2}{9}) - 2 }{ \frac{2}{9} + 1}$

          $= \frac{14 - 18}{9} * \frac{9}{2 + 9}$

               $= \frac{-4}{11}$



Hope this helps!

Answer 2

hope it helps you...........