Question

what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10)
and B(3,-8)​

Answer 1

Question:-

what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10)

and B(3,-8)

SoLuTiOn:-

( Full Steps )

Let C (-8,3) divides the line segment AB in the ratio m : n

$x = \frac{mx {}^{2} + mx {}^{1} }{m + n} and$

$\frac{my2 + my1}{m + n}$

Here,

( X,Y) = ( -8,3 );( X1,Y1) = ( 2,-2 )

And ( X2,Y2 ) = (-4,1 )

So,

$- 8 = \frac{m( - 4) + n(2)}{m + n} and$

$3 = \frac{m(1) + n( - 2)}{m + n}$

⭐ -8m - 8n = -4m + 2n

and 3m + 3n = m - 2n

⭐ -8m + 4m -8n -2n = 0

and 3m - m + 3n + 2n = 0

⭐ -4m -10n = 0 and

2m + 5n = 0

⭐ -2m -5n = 0 and

2m + 5n = 0

⭐ 2m + 5n = 0 and

2m + 5n = 0

⭐ 2m = -5n

$= \frac{m}{n} = \frac{ - 5}{2}$

Hence, the ratio is 5:2 and this negative sign shows that the division is external.

Answer Completed ✔️

System solved ✔️

Free From Doubt✔️