Which option correctly gives the coordinates of a point P that divides the line…

MATHEMATICS · Single correct · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Which option correctly gives the coordinates of a point P that divides the line segment joining A

(x_1, y_1)

and B

(x_2, y_2)

internally in the ratio

m:n

? (a)

P\Bigl(\tfrac{m x_1 + n x_2}{m+n},\, \tfrac{m y_1 + n y_2}{m+n}\Bigr)

(b)

P\Bigl(\tfrac{x_1 + x_2}{2},\, \tfrac{y_1 + y_2}{2}\Bigr)

(c)

P\Bigl(\tfrac{m x_2 + n x_1}{m+n},\, \tfrac{m y_2 + n y_1}{m+n}\Bigr)

(d)

P\Bigl(\tfrac{m x_2 + n x_1}{m-n},\, \tfrac{m y_2 + n y_1}{m-n}\Bigr)