Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

A.

3√10

B.

3√5

C.

√26

D.

√13

Correct answer is D

2x - y .....(i)

x + y.....(ii)

from (i) y = 2x - 4

from (ii) y = -x + 2

2x - 4 = -x + 2

x = 2

y = -x + 2

= -2 + 2

= 0

\(x_1\) = 2

\(y_1\) = 0

\(x_2\) = 4

\(y_2\) = 3

Hence, dist. = \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\)

= \(\sqrt{(3 - 0)^2 + (4 - 2)^2}\)

= \(\sqrt{3^2 + 2^2}\)

= \(\sqrt{13}\)