First slide

Equation of line in Straight lines

Question

$T h e l e n g t h o f t h e a l t i t u d e t h r o g u h A o f t h e t r i a n g l e A B C w h e r e A (- 3, 0), B (4, - 1), C (5, 2) i s \frac{22}{\sqrt{k}} t h e n k =$

Moderate

A

$10$
B

$5$
C

$\sqrt{10}$
D

$\sqrt{5}$

Solution

$E q u a t i o n o f t h e l i n e j o i n i n g t h e p o i n t s B a n d C i s y - y_{1} = m (x - x_{1}) y + 1 = 3 (x - 4) \Rightarrow y + 1 = 3 x - 12 \Rightarrow 3 x - y - 13 = 0 T h e l e n g t h o f t h e a l t i t u d e f r o m A t o t h e l i n e B C i s t h e p e p e n d i c u l a r d i s \tan c e f r o m A t o t h e l i n e B C i t i s e q u a l t o |\frac{a x_{1} + b y_{1} + c}{\sqrt{a^{2} + b^{2}}}| = |\frac{3 (- 3) - 1 (0) - 13}{\sqrt{9 + 1}}| = \frac{22}{\sqrt{10}}$
$C o m p a r i n g t h e a l t i t u d e l e n g t h w i t h \frac{22}{\sqrt{k}}, k = 10$

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