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

C

Explanation

Slope of AB `=(5-(-4))/(-4+1) = -3`
`therefore " Equation of AB" -=3x+y+7=0 " " (1)`
`"Slope of CF" = (1)/(3)`
`therefore " Equation of "CF-=x-3y-11=0 " " (2)`
`"Slope of AC" = (5-1)/(-4-4) = -(1)/(2)`
`therefore " Equation of " AC-=x+2y-6=0 " " (3)`
`"Slope of " BE-=2`
`therefore " Equation of "BE-= 2x-y-7=0 " " (4)`
Solving (1) and (4), we get `B-=(0,-7).`
Solving (2) and (3), we get `C-=(8,-1).`
`"Slope of " BC=(-7+1)/(0-8) = (3)/(4)`
`therefore " Equation of " BC-=3x-4y-28=0`