Question

If angle between the two lines is 45° and slope of one line is 1/4 then which of the following is possible value of the slope of other line.

(a) 3/5

(b) -3/5

(c) -5/3

(d) 4/5

This question was posed to me during an online exam.

My query is from Various Forms of the Equation of a Line topic in division Straight Lines of Mathematics – Class 11

Answer 1

Correct answer is (b) -3/5

Easy explanation: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|

tan 45° = \(|\frac{m-1/4}{1+m/4}|\)

=> \(\frac{4m-1}{m+4}\) = -1

=>- m-4 = 4m-1 => 5m = -3

=> m = -3/5.