question_answer

List-II gives the coordinates of the point P that divides the line segment joining the points in the given ratio given in List-I, match them correctly.

	List - I		List - II
P.	A(-1, 3) and B (-5, 6) internally in the ratio 1 : 2	1.	(7, 3)
Q.	A (-2, 1) and B (1, 4) internally in the ratio 2 : 1	2.	(0, 3)
R.	A (1, 7) and B (3, 4) internally in the ratio 3 : 3	3.	\[\left( \frac{11}{5},\frac{26}{5} \right)\]
S.	A (4, -3) and B (8, 5) internally in the ratio 3 : 1	4.	\[\left( -\frac{7}{3},\,4 \right)\]

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

Correct Answer: A

Solution :

(P)

\[x=\frac{-5-2}{3}=-\frac{7}{3}\Rightarrow \,\,y=\frac{6+6}{3}=4\]

\[\therefore\]  Point P is \[\left( \frac{-7}{3},\,4 \right)\]

(Q)

\[x=\frac{2-2}{2+1}=0,\,y=\frac{8+1}{2+1}=3\]

\[\therefore\] Points P is (0, 3)

[R]

\[x=\frac{9+2}{5}=\frac{11}{5},\,y=\frac{12+14}{5}=\frac{26}{5}\]

\[\therefore\] Points P is \[\left( \frac{11}{5},\,\frac{26}{5} \right)\]

(S)

\[x=\frac{24+4}{3+1}=7,\,y=\frac{15-3}{3+1}=3\]

\[\therefore\] Point P is (7, 3)