ABCD is a square, AC is a diagonal. If the coordinate of A, C are (− 5, 8) and (7, − 4) . Find the coordinate of B and D.


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Question Number 58984 by Tawa1 last updated on 02/May/19

$ABCD is a square, AC is a diagonal . If the coordinate of A, C$ $are (- 5, 8) and (7, - 4) . Find the coordinate of B and D .$
	Answered by tanmay last updated on 02/May/19

	$A C e q n (y - 8) = \frac{8 + 4}{- 5 - 7} (x + 5)$ $y - 8 = - x - 5$ $x + y = 3 \to y = - x + 3$ $s l o p e m = (- 1)$ $t h e e q n o f s t l i n e p a s s i n g t h r o u g h (- 5, 8)$ $y - 8 = m_{1} (x + 5)$ $t h e a n g l e b e t w e e n x + y = 3 a n d (y - 8) = m_{1} (x + 5)$ $i s 45^{0}$ $t a n 45^{o} = \frac{m_{1} - (- 1)}{1 + m_{1} (- 1)}$ $m_{1} + 1 = 1 - m_{1} m_{1} = 0$ $s o e q n i s (y - 8) = 0 \times (x + 5)$ $y = 8 \leftarrow e q n o f A D$ $t h e e q n ∥ t o y = 8 p a s s i n g t h r o u g h (7, - 4) i s$ $y = - 4 \to e q n o f B C$ $s o e q n o f A B x = - 5 ($ $e q n o f C D i s x = 7$ $s o A B \to x + 5 = 0$ $C D i s x - 7 = 0$ $B C i s y + 4 = 0$ $D A i s y - 8 = 0$ $A (- 5, 8) B (- 5, - 4) C (7, - 4) D (7, 8)$
	Commented by Tawa1 last updated on 02/May/19

	$God bless you sir$
	Commented by tanmay last updated on 02/May/19

	$t h a n k y o u . . .$
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