The distance between the point (4, 3) and the intersection of y = 2x +…

The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 – x is

Correct Answer: Option B

Explanation

P₁ (4, 3), P₂ (x, y)
y = 2x + 4 …..(1)
y = 7 – x …..(2)
Substitute (2) in (1)
7 – x = 2x + 4
7 – 4 = 2x + x
3 = 3x
x = 1
Substitute in eqn (2)
y = 7 – x
y = 7 – 1
y = 6
P₂ (1, 6)
Distance between 2 points is given as
D = (sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2})
D = (sqrt{(1 – 4)^2 + (6 – 3)^2})
D = (sqrt{(-3)^2 + (3)^2})
D = (sqrt{9 + 9})
D = (sqrt{18})
D = (sqrt{9 times 2})
D = (3sqrt{2})

There is an explanation video available below.