a(-1,1),b(5,3) are opposite vertices of a square.the equation of the other diagonal (not passing through a,b) of a square is?

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Solution

Dear student
$G i v e n : H e r e, A B i s t h e d i a g o n a l o f s q u a r e . T h e v e r t i c e s o f a s q u a r e A (- 1, 1) a n d B (5, 3) L e t t h e m i d - p o i n t o f A B b e E T h e n c o o r d i n a t e s o f E a r e (\frac{1 + 3}{2}, \frac{- 1 + 5}{2}) = (2, 2) T h e r e f o r e e q u a t i o n o f o t h e r d i a g o n a l i s y - y_{1} = m (x - x_{1}) \Rightarrow y - 2 = \frac{- 1}{\frac{3 - 1}{5 + 1}} (x - 2) \Rightarrow y - 2 = \frac{- 6}{2} (x - 2) \Rightarrow y - 2 = - 3 (x - 2) \Rightarrow y - 2 = - 3 x + 6 \Rightarrow y + 3 x - 8 = 0$
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