Question

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

(a) 2

(b) -4

(c) 1

(d) -2

 

 

Answer 1

Given points are P(1, 4) and Q (k, 3).

Slope of PQ, m1 = (y2 – y1)/(x2 – x1)

= (3 – 4)/(k – 1)

= -1/(k -1)

Slope of the perpendicular line, m2 = (k – 1) (because m1m2 = -1)

 

Midpoint of PQ = ((k+1)/2, (3+4)/2)

= ((k+1)/2, 7/2)

The perpendicular line passes through the midpoint ((k+1)/2, 7/2).

The required equation of line is y – y1 = m(x- x1)

y – 7/2 = (k -1)(x – (k+1)/2)

Given that perpendicular bisector has y intercept = -4

At x = 0,y = -4

So -4 – 7/2 = (k -1)(0 – (k+1)/2)

-15/2 = -(k²– 1)/2

k² – 1 = 15

k² = 16

 k = ±4

 

 

The value of k is -4.