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Angle between Two Line Segments

Mid-points of...

Question

Mid-points of the sides AB and AC of a $△$ ABC are (3, 5) and (-3, -3) respectively, then the length of the side BC is :

A

10

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B

20

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C

15

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D

30

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Solution

The correct option is B $20$
$G i v e n - A B C i s a t r i a n g l e . T h e m i d p o i n t o f A C i s P a n d t h a t o f A B i s Q . t o f i n d o u t - t h e l e n g t h o f P Q = ? S o l u t i o n - W e s h a l l u s e t h e m i d p o i n t t h e o r e m w h i c h s a y s, t h e l i n e j o i n i n g t h e m i d p o i n t s o f t h e t w o s i d e s o f a t r i a n g l e, i s p a r a l l e l t o a n d h a l f t h e t h i r d s i d e . ∴ 2 P Q = B C . N o w P (x_{1}, y_{1}) = (3, 5) a n d Q (x_{2}, y_{2}) = (- 3, - 3) . ∴ U s i n g d i s t a n c e f o r m u l a, P Q = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(3 + 3)}^{2} + {(5 + 3)}^{2}} u n i t s = 10 u n i t s . ∴ B C = 2 P Q = 2 \times 10 u n i t s = 20 u n i t s . A n s - O p t i o n B .$

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