First slide

Equation of line in Straight lines

Question

If AD, BE and CF are the altitudes of $∆$ ABC whose vertex A is the point (-4, 5). Also, the coordinates of the points E and F are (4,1)
and (-1, -4) respectively. Then, equation of BC is

Easy

A

$3 x - 4 y + 28 = 0$
B

$4 x + 3 y + 28 = 0$
C

$3 x - 4 y - 28 = 0$
D

$x + 2 y + 7 = 0$

Solution

$Slope of A B = \frac{5 - (- 4)}{- 4 + 1} = - 3$
$∴ Equation of A B \equiv 3 x + y + 7 = 0 - - - - - - - - (i)$
$Slope of C F = \frac{1}{3}$
$∴ Equation of C F : x - 3 y - 11 = 0 - - - - (i i)$
$Slope of A C = \frac{5 - 1}{- 4 - 4} = - \frac{1}{2}$
$∴ Equation of A C : x + 2 y - 6 = 0 - - - - (i i i)$
Slope of BE - 2
$∴ Equation of B E : 2 x - y - 7 = 0 - - - (i v)$
$Solving (i) and (iv), we get B \equiv (0, - 7)$
$Solving (ii) and (iii), we get C \equiv (8, - 1)$
$Slope of B C = \frac{- 7 + 1}{0 - 8} = \frac{3}{4}$
$∴ Equation of B C : 3 x - 4 y - 28 = 0$

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