The points A,B,C have coordinates (3,1),(1,5),(5,7) a) find the line l_1 joining the points A and B b)Find the line l_2 perpendicular to l_1 and passes through the point B c) show that the point C lie on the line l_(2 ) hence or otherwise find the area of the triangle ABC.


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Question Number 35208 by Rio Mike last updated on 16/May/18

$T h e p o i n t s A, B, C h a v e c o o r d i n a t e s$ $(3, 1), (1, 5), (5, 7)$ $a) f i n d t h e l i n e l_{1} j o i n i n g t h e p o i n t s$ $A a n d B$ $b) F i n d t h e l i n e l_{2} p e r p e n d i c u l a r$ $t o l_{1} a n d p a s s e s t h r o u g h t h e p o i n t$ $B$ $c) s h o w t h a t t h e p o i n t C l i e o n t h e$ $l i n e l_{2} h e n c e o r o t h e r w i s e f i n d$ $t h e a r e a o f t h e t r i a n g l e A B C .$
	Answered by ajfour last updated on 16/May/18

	$y - 1 = (\frac{1 - 5}{3 - 1}) (x - 3)$ $\Rightarrow y = 7 - 2 x$ $y - 5 = \frac{1}{2} (x - 1)$ $\Rightarrow 2 y = x + 9$ $2 y = 5 + 9 = 2 \times 7$ $△ = \frac{1}{2} ∣ \| \begin{matrix} 3 & 1 & 1 \\ 1 & 5 & 1 \\ 5 & 7 & 1 \end{matrix} \| ∣$ $= \frac{1}{2} ∣ - 6 + 4 - 18 ∣ = 10 s q . u n i t s .$
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