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-

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 \dots

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