Question

Co-ordinates of the point dividing internally the line segment joining the points (4, -3) and (9, 7) in the ratio 3 : 2 are

(A) (7, 3)

(B) (3, 7)

(C) (5, 7)

(D) (7, 5)

Answer 1

Correct option is (A) (7, 3)

Let the point which divide A(4, - 3) and B(9, 7) in the ratio 3 : 2

We know that by section formula, the Co-ordinates of the points which divide internally the line Segment joining the point \((x_1, y_1)\) and \((x_2, y_2)\) in the ratios m : n

(x, y) = \((\frac{mx_2+nx_1}{m+n} . \frac{my_2+ny_1}{m+n})\)  

Here, \(x_1=4,\ y_1=-3,\ x_2=9,\ y_2=7\ \text{and}\ m :n =3:2\ \)   

So, 

\(x = (\frac{mx_2+nx_1}{m+n})\)    

\(= (\frac{3\times9\ +\ 2\times4}{3+2})\)  

\(= (\frac{27+8}{5})\)  

\(= \frac{35}{5}\)  

= 7 

\(y= (\frac{my_2+ny_1}{m+n})\)    

\(y= (\frac{3\times7+2\times(-3)}{3+2})\)   

\(y= \frac{21-6}{5}\)    

\(=\frac{15}{5}\)  

= 3

Hence, the coordinate of the point P is (7, 3).