Question

determine the ratio in which the point p(m,6) divides the join of A(4,3) and B(2,8)also,find the value of N.​

Answer 1

Answer:

the value of m=14/5 and the ratio m:n=2:3

Answer 2

Step-by-step explanation:

Solutions ::

......................................

Given,

p(m,6) divides the join of A(4,3) and B(2,8)

To find,

the value of N=??

$by \: midpoint \: theorem =$

$x = \frac{x1 +x2 }{2}$

$y = \frac{y1 + y2}{2}$

$x = \frac{4 + 2}{2} = 3.....(1)$

$y = \frac{3 + 8}{2} = \frac{11}{2} ......(2)$

By using section formula

$x = \frac{mx1 + nx2}{m + n} \: . \: \: \: y = \frac{my1 + ny2}{m + n}$

$m = \frac{4m + 2n}{m + n}$

$6 = \frac{m 3 + n8}{m + n}$

${m}^{2} + mn = 4m + 2n ......(3)$

$6m + 6n = 3m + 8n$

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

$3m - 2n = 0$

$m = \frac{2n}{3} .....(4)$

now put the value of eqn (4) In eqn (3)

${m}^{2} + mn - 4m - 2n = 0$

$\frac{ {(2n}^{2} )}{3} + \frac{2n}{3} \times n - 4( \frac{2n}{3} ) - 2n = 0$

$\frac{4 {n}^{2} }{9} + \frac{8 {n}^{2} }{3} - \frac{8n}{3} - 2n = 0$

$\frac{24 {n}^{2} + 4 {n}^{2} }{9} - \frac{8n}{3} - 2n = 0$

$\frac{28 {n}^{2} }{9} - \frac{8n - 6n}{ 3} = 0$

$\frac{28 {n}^{2} }{9} - \frac{14n}{3 } = 0$

$\frac{28 {n}^{2} }{9} = \frac{14n}{ 3}$

$\frac{2n}{3} = 1$

$n = \frac{3}{2}$

$m = \frac{2n}{3} ....(4)$

put n value in equations (4)

$m = \frac{2n}{3}$

$m = \frac{2}{3} \times \frac{3}{2} = 1$

the ratio will be m=1 and n=3/2

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