Question

Find the ratio in which point P (-1, y) lying on the line segment joining points A (-3, 10) and B (6, -8) divides it. Also find the value of y.



pls answer!!!!​

Answer 1

Step-by-step explanation:

Answer::

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

$- 1 = \frac{m( - 3) + n(6)}{m + n}$

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

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

$2m - 7n = 0...........(1)$

$y = \frac{m(10) + n( - 8)}{m + n}$

$my + ny = 10m - 8n$

$my + ny - 10m + 8n = 0 .....(1)$

$m(y - 10) + n(y + 8) = 0$

solve both equations (1) and (2 )

by linear equation

by midpoint theorem we get y values

y=y1+y2/2=10-8/2=1

now this value in second equations

m(1)+n(1)-10m+8n=0

-9m+9n=0

m-n=0......(3)

now, solve like linear equations

2m-7n=0

2m-2n=0

5m=0

m=0

2(0)-7n=0

n=0