Find the distance between the point Q (4,3) and the point common to the lines…

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

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
x₁ = 2₁
y₄ = 0₁
x₂ = 4₁
y₂ = 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})