Question

If line joining (1, 2) and (7, 6) is perpendicular to line joining (3, 4) and (11, x).

(a) 12

(b) 16

(c) -16

(d) -12

I have been asked this question in an online interview.

My doubt stems from Various Forms of the Equation of a Line topic in portion Straight Lines of Mathematics – Class 11

Answer 1

Right option is (c) -16

Easy explanation: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).

Lines are perpendicular means m1*m2 = -1

=> \((\frac{x-4}{11-3})(\frac{6-2}{7-1})\) = -1

=> (x-4)(4) = (-1)(8)(6)

=> x-4 = -12 => x= -16.