Question

If point P(-4, 6) divides the line segment AB with A(-6, 10) and B(r, s) in
the ratio 2:1, find the co-ordinates of B.​

Answer 1

Answer:

see the attachment

it is solved by ghe section formula of coordinate geometry

Answer 2

The co-ordinates of B are (-3,4) .

Step-by-step explanation:

Section formula : If a point (x,y) divides a line segment having end points $(x_1,y_1)$ and $(x_2,y_2)$  in ratio of m : n  , then the coordinate of that point is given by :-

$x=\dfrac{mx_2+mx_1}{m+n}$

$y=\dfrac{my_2+my_1}{m+n}$

Given : If point P(-4, 6) divides the line segment AB with A(-6, 10) and B(r, s) in

the ratio 2:1.

Then $-4=\dfrac{2r+1(-6)}{2+1}$

$6=\dfrac{2s+1(6)}{2+1}$

$-4=\dfrac{2r-6}{3}$     $6=\dfrac{2s+10}{3}$

$2r-6=-4(3)$     $2s+10=3(6)$

$2r-6=-12$     $2s+10=18$

$2r=-12+6$     $2s=18-10$

$2r=--6$     $2s=8$

$r=-3$     $s=4$

Hence, the co-ordinates of B =  (-3,4)

# Learn more :

The coordinates of midpoint of line joining the points A and B are two, -3 if coordinates of point a r - 3, 4 then find coordinates of point B​

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