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

A.

\(\sqrt{13}\)

B.

\(3\sqrt{2}\)

C.

\(\sqrt{26}\)

D.

\(10\sqrt{5}\)

Correct answer is B

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 = \(3\sqrt{2}\)