First slide

Equation of line in Straight lines

Question

ABC is an isosceles triangle. If the coordinates of the base are. $B (1, 3)$ ) and, $C (- 2, 7)$ , the coordinates of vertex A can be

Moderate

A

$(1, 6)$
B

$(- \frac{1}{2}, 5)$
C

$(\frac{5}{6}, 6)$
D

$(3, 7)$

Solution

$G i v e n t h a t t h e t r i a n g l e A B C i s I s o s c e l e s t r i a n g l e, A i s a t e q u a l s i d e s f r o m t h e v e r t i c e s B a n d C S o t h a t a n y p o i n t o n t h e p e r e p e n d i c u l a r b i s e c t o r o f B C e x c e p t t h e m i d p o i n t o f B C i s A T h e m i d p o i n t o f B C i s (- \frac{1}{2}, 5) T h e p e r p e n d i c u l a r b s i e c t o r o f B C i s y - 5 = \frac{3}{4} (x + \frac{1}{2}) 4 y - 20 = 3 x + \frac{3}{2} 6 x - 8 y - 43 = 0 V e r i f y t h e o p t i o n s t o g e t t h e v e r t e x A$

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