The equation of the line bisecting perpendicularly the segment joining the points (-4,6) and (8,8) is

Options

A. 6x +y -19=0
B. y=7
C. 6x + 2y -19=0
D. x+2y-2=0

Answer

A

Explanation

Equation of the line passing through (-4,6) and (8,8) is
` (y-6) = ((8-6)/(8+4))(x+4)`
` Rightarrow 6y -x-40=0`
Since, equation of any line, which is perpnedicular to Eq. (i) is
`6x +y+lambda=0`
Since, this line passes through the mid-point of (-4,6) and (8,8) which is `((-4+8)/2, (6+8)/2) i.e, (2,7)`
`6 xx 2 +7+ lambda = 0 Rightarrow lambda = -19`
On putting ` lambda = -19` in Eq. (ii) we get the required line which is 6x+y -19=0