Question

If the perpendicular bisector of the line segment joining P(1, 4) and Q(α, 3) has y-intercept -4, then a possible value of is

(A)   -2

(B)   -4

(C)   1

(D)   2

Answer 1

Correct option  (B)  -4 

Explanation :

Since every point (x, y) on the perpendicular bisector of (bar)PQ is equidistant from both P and Q we have

Therefore, equation of the perpendicular bisector of (bar) PQ is

2(α - 1)x + 8 = 2y + α²

Hence -4 = y-intercept = 8 - α²/2

Therefore, α² = 16 = ±4