First slide

Equation of line in Straight lines

Question

The vertices of a triangle are $A (- 1, - 7), B (5, 1) a n d C (1, 4)$ . The equation of the bisector of $∠ A B C$ is:

Difficult

A

$7 x + y - 36 = 0$
B

$x - 7 y + 2 = 0$
C

both (a) and (b)
D

neither (a) nor (b)

Solution

Bisector $B D$ of $∠ A B C$ divides $A C$ in $2 : 1$
$∴$        $D = (1 / 3, 1 / 3)$ .
$∴$     Equation of $B D$ is $y - 1 = \frac{2 / 3}{14 / 3} (x - 5)$
$\Rightarrow$      $x - 7 y + 2 = 0$ .

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