First slide

Equation of line in Straight lines

Question

If AD, BE and CF are the altitudes of a triangle ABC whose vertex A is the point (-4, 5). The coordinates of the points E and F are (4,1) and (-1, -4) respectively, then equation of BC is

Moderate

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

$\begin{aligned} Slope of A F = \frac{5 - (- 4)}{- 4 + 1} = \frac{9}{- 3} = - 3 \\ ∴ Slope of C F = \frac{1}{3} \end{aligned}$
$∴ Equation of C F is x - 3 y - 11 = 0 - - - - - (1)$
$\begin{array}{l} Slope of A E = \frac{5 - 1}{- 4 - 4} = \frac{4}{- 8} = - \frac{1}{2} \\ ∴ Slope of B E = 2 \end{array}$
$∴ Equation of B E is 2 x - y - 7 = 0 - - - - (2)$
$Solving (i) and (ii), we get point O = (2, - 3)$
$Equation of A C is x + 2 y - 6 = 0 - - - - (3)$
$Solving (i) and (iii) we get point C (8, - 1)$
$Also slope of A O is \frac{- 4}{3}$
$∴ Slope of B C is \frac{3}{4}$
$∴ Equation of B C is 3 x - 4 y - 28 = 0$

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