Question

Find the ratio in which the point P(m, 6) divides the line segment joining the points A(-4, 3) and B(2, 8). Also find the value of m. detailed long answer required

Answer 1

Answer:

m=-4m+2n/m+n

m²+mn=-4m+2n

m²+4m+mn+2n

m²+4m+n(m+2)=0

use formula method u get urs answer

Step-by-step explanation:

6=3m+8n/m+n

6m+6n-3m-8n=0

3m-2n=0

Answer 2

Answer

Ratio => 3/2:1

Value of m => -3/5

Formula

Coordinates of point:

$\bf \: \: \: x = \dfrac{m x_{2} +n x_{1} }{m + n}$

$\bf \: \: \: y = \dfrac{m y_{2} +n y_{1} }{m + n}$

Solution

Let the ratio in which point P divides the line segment be k:1.

Coordinates of P will be,

$\bf \: P( x,y ) = > ( \dfrac{2k - 4}{k + 1} \: , \: \dfrac{8k + 3}{k + 1} )$

Given, the coordinates of P as (m,6)

$\sf \: \dfrac{2k - 4}{k + 1} = m \\ \sf \: 2k - 4 = m(k + 1) \\ \sf \: 2k - 4 = km + m....eq(1)$

$\sf\dfrac{8k + 3}{k + 1} = 6 \\ \\ \sf \: 8k + 3 = 6k + 6 \\ \\ \sf \: 2k = 3 \\ \\ \sf \: k = \dfrac{3}{2}$

$\therefore \sf \: ratio \: is \: \implies \boxed{ \red{ \frac{3}{2} :1}}$

Now, put k=3/2 in eq(1),

$\sf \: 2k - 4 = km + m \\ </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\sf \: 2 \times \frac{3}{2} - 4 = \frac{2}{3} \times m + m \\ </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\sf \: 3 - 4 = \frac{2m}{3} + m \\ </strong><strong>\</strong><strong>\</strong><strong> \sf \: - 1 = \dfrac{2m + 3m}{3} \\ </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\sf - 3 = 5m \\ </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\sf \: \boxed{ \red{m = \frac{ - 3}{5} }}$