Question

Find the ratio in which (m,6) divides line joining (-4,3) and (2,8). Also find m. who will give the correct answer i will mark brainlist..

Answer 1

Let the given points be A(-4,3) and B(2,8) and C(m,6).

Let the ratio be k:1.

Now,

m1 = k, m2 = 1.

x1 = -4, y1 = 3, x2 = 2, y2 = 8, x = m,y = 6.


Now,

x = m1x2 + m2x1/m1 + m2,

m = k * 2 + 1 * (-4)/k + 1

m = 2k - 4/k + 1   ------- (1)


Now,

y = m1y2 + m2y1/m1 + m2

6 = k * 8 + 1 * 3/k + 1

6 = 8k + 3/k + 1 

6(k + 1) = 8k + 3

6k + 6 = 8k + 3

6k - 8k = 3 - 6

-2k = -3

k = 3/2.

Substitute k = 3/2 in (1), we get

m = 2k - 4/k + 1

m = 2(3/2) - 4/(3/2) + 1

m = 3 - 4/5/2

m = -1/5/2

m = -2/5.



Hope this helps!

Answer 2

here

(-4,3). and (2,8)

x1 = -4

x2 = 2

y1 = 3

y2 = 8
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p(x,y) = [ mx2 + nx1/m+n , my2 + ny1/m+n]

p(m,6) = [2m - 4n/m+n , 8m + 3n/m+n]

compare both side

6 = 8m+3n/m+n

6(m+n) = 8m+3n

6m + 6n = 8m + 3n

6m - 8m = 3n -6 n

-2m = -3n

m/n = -3/-2

m/n = 3/2

m:n = 3:2
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m = 2m-4n/m+n

m(m+n) = 2m-4n

m(3+2) = 2(3)-4(2)

m(5) = 6-8

5m = -2

m = -2/5
_______________________________________________________________

so ratio is

3:2

and

m = -2/5