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: Option D
Explanation
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_{1}
y_{4} = 0_{1}
x_{2} = 4_{1}
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})