Question

Find the ratio in which the point (–3, p) divides the line segment joining the points (–5, –4) and B (–2 , 3 ). Hence find the value of p.

Answer 1

Step-by-step explanation:

let the point A(-5, -4) and B(-2, 3) which divides the linesegment AB at the point O( -3, p) in the ratio m:n .

formula : [mx2+nx1 /m+n , my2+ny1 /m+n]

[m(-2) + n(-5) /m+n , m(3) + n(-4) /m+n]

[-2m-5n /m+n , 3m-4n /m+n]

So, X = -2m-5n /m+n and Y = 3m-4n /m+n

-3 = -2m-5n /m+n and p = 3m-4n /m+n

-3m-3n = -2m-5n and p(m+n) = 3m-4n

-3m+2m = -5n+3n and p(m+n) =3m-4n

-m = -2n

m = 2n

So, put the value m = 2n in p(m+n) = 3m-4n

p( 2n +m/2) = 3(2n) - 4(m/2)

p/2( 4n+m) = 6n -2m

p/2 = 6n-2m /4n+m

p = 2 (6n-2m /4n+m)

Hence, p = 12n-4m / 4n+m