If AD, BE and CF are the altitudes of `Delta ABC` whose vertex A is (-4,5). The coordinates of points E and F are (4,1) and (-1,-4), respectively. Equation of BC is

Options

A. `3x - 4y - 28 = 0`
B. `4x +3y - 28 = 0`
C. `3x - 4y +28 = 0`
D. `x +2y +7 = 0`

Answer

A

Explanation

Slope of `AF = (5-(-4))/(-4+1) = (9)/(-3) =- 3`
`:.` Slope of `CF = (1)/(3)`
`:.` Equation of CF is `x - 3y - 11 = 0` (i)
Slope of `AF =(5-1)/(-4-1) = (4)/(-8) =- (1)/(2)`
`:.` Slope of `BE = 2`
`:.` Equation of BE is `2x - y - 7 = 0` (ii)
Solving (i) and (ii), we get point `O =(2,-3)`
Equation of AC is `x+2y - 6 = 0` (iii)
Solving (i) and (iii) we get point `C (8,-1)`
Also slope of AO is `-4//3`
`:.` Slope of BC is `3//4`
`:.` Equation of BC is `3x - 4y - 28 = 0`