Question

List - II Gives the coordinates of a point P that divides the line segment AB joining the points given in List -I, match them correctly.
$\begin{array}{cccc}& List-I& & ListII\\ \left(P\right)& A(-1,3)andB(-5,6)Internallyintheratio1:2& \left(1\right)& (7,3)\\ \left(Q\right)& A(-2,1)andB(1,4)internallyintheratio2:1& \left(2\right)& (0,3)\\ \left(R\right)& A(1,7)andB(3,4)internallyintheratio3:2& \left(3\right)& (\frac{11}{5},\frac{26}{5})\\ \left(S\right)& a(4,-3)andB(8,5)internallyintheratio3:1& \left(4\right)& (-\frac{7}{3},4)\end{array}$

• A. P- 4, Q-2, R-3, S-1
• B. P- 3, Q-2, R-4, S-1
• C. P- 1, Q-4, R-3, S-2
• D. P- 3, Q-1, R-2, S-4

Answer 1

The correct option is A P- 4, Q-2, R-3, S-1

(P)
$\because$ The point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n is , $(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

$\therefore x=\frac{-5-2}{3}=-\frac{7}{3}\text{and}y=\frac{6+6}{3}=4$
$\therefore$ Point is $(\frac{-7}{3},4)$

(Q)

$\because$ The point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n is , $(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

$\therefore x=\frac{2-2}{2+1}=0,\text{and}y=\frac{8+1}{2+1}=3$
$\therefore$ Point is (0,3)

(R)
$\because$ The point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n is , $(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

$\therefore x=\frac{9+2}{5}=\frac{11}{5},$
and $y=\frac{12+14}{5}=\frac{26}{5}$
$\therefore$ Point is $(\frac{11}{5},\frac{26}{5})$

(S)
$\because$ The point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n is , $(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

$\therefore x=\frac{24+4}{3+1}=7$,
and $y=\frac{15-3}{3+1}=3$
$\therefore$ Point is (7,3)