Question

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept  – 4. Then a possible value of k is

(a) – 4

(b) 1

(c) 2

(d) – 2

Answer 1

The correct option (a) – 4   

Explanation:

slope of PQ = [(3 – 4)/(k – 1)] = [(– 1)/(k – 1)]

∴ slope of AB = – [1/{(– 1)/(k – 1)}] = k – 1

R is midpoint of PQ

∴ R = [{(k + 1)/2}, (7/2)]

equation of AB can be written as

y – (7/2) = (k – 1)[x – {(k + 1)/2}]

∴ – 4 – (7/2) = (k – 1)[(k + 1)/2](– 1)

∴ 15 = k² – 1

∴ k² = 16

∴ k = ± 4