Question

List II mentions the distance between the pairs of points given in List I. Match the columns.

	List I		List II
P	$(-5,7),(-1,3)$	1	$5$
Q	$(5,6),(1,3)$	2	$\sqrt{8}$
R	$(\sqrt{3}+1,1),(0,\sqrt{3})$	3	$\sqrt{6}$
S	$(0,0),(-\sqrt{3},\sqrt{3})$	4	$4\sqrt{2}$

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

Answer 1

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

(P): Distance between the points $(-5,7),(-1,3)$
$=\sqrt{(-1+5{)}^2+(3-7{)}^2}$
$=\sqrt{16+16}=4\sqrt{2}$

(Q): Distance between the points $(5,6),(1,3)$
$=\sqrt{(1-5{)}^2+(3-6{)}^2}$
$=\sqrt{16+9}=5$

(R): Distance between the points $(\sqrt{3}+1,1),(0,\sqrt{3})$
$=\sqrt{[0-(\sqrt{3}+1){]}^2+(\sqrt{3}-1{)}^2}$
$=\sqrt{(\sqrt{3}+1{)}^2+(\sqrt{3}-1{)}^2}$
$=\sqrt{3+2\sqrt{3}+1+3-2\sqrt{3}+1}$
$=\sqrt{6+2}$
$=\sqrt{8}$

(S): Distance between the points $(0,0),(-\sqrt{3},\sqrt{3})$
$=\sqrt{(-\sqrt{3}{)}^2+(\sqrt{3}{)}^2}=\sqrt{3+3}=\sqrt{6}$

Therefore, P - 4, Q - 1, R - 2, and S - 3.