Question

Find the coordinates of the point which divides the join of

(-1, 7) and (4, -3) in the ratio 2:3​

Answer 1

Answer:

given

m= 2, n = 3

(x1,y1) = (-1,7)

(x2,y2) = (4,-3)

now, it is not given, whether the point divides the line internally or externally. So we assume both

1. point divides internally

the coordinate of dividing point is given by

(mx2+nx1)/(m+n), (my2+ny1)/(m+n)

((2*4+3*-1)/(2+3), (2*-3+3*7)/(2+3))

((8 -3)/5, (-6+21)/5)

(5/5, 15/5)

(1, 3)

2. point divides externally

the coordinate is given by

(mx2 - nx1)/(m-n), (my2 - ny1)/(m - n)

((2*2 - 3*-1)/(2-3), (2*-3 - 3*7)/(2-3))

((4+3)/(-1), (-6-21)/(-1))

(7/(-1), -27/(-1))

(-7, 27)