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

Options

A. `-4`
B. 1
C. 2
D. `-2`

Answer

A

Explanation

Since slope of PQ = `( 4-3)/(1-k) = 1/(1-k) `
slope of AM = (k-1)

Equation of AM is
` y - 7/2 = (k -1) [x - ((k+1)/2)]`
For y-intercept , when x=0 m y=-4 then
`-4-7/2 = - (k-1) ((k+1)/2)`
` Rightarrow 15/2 = (k^(2)-1)/(2) Rightarrow k^(2) -1=15`
` k = -+ 4`