Question

if A(x,y) is equidistant from the points (-4,3) and (3,-4) then show that x=y

Answer 1

See the picture.
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Just one correction
SA=PA

Answer 2

hi mate here is ur answer

given that A(x,y) is equidistant from

B( -4,3) and C ( 3,-4)

to prove that x = y

using distance formula

√(x1 - x2)^2 + (y1-y2)^2

the distance between ab = ac

the distance of ab

= √(x+4)^2 + (y-3)^2 eq.1

the distance of ac

√(x-3)^2 + (y+4)^2 eq.2

squaring on both sides

we get ,

(x+4)^2 + (y-3)^2 = (x-3)^2+ (y + 4)^2

expanding the identities

x^2 + 16 + 8x + y^2 + 9-6y = x^2 + 9 -6x + y^2 + 16 + 8y

8x- 6y = -6x + 8y

bringing x terms and y terms separately

we get,

8x + 6x = 8y + 6y

14x = 14 y

x = y

hence proved

hope it helps!!!

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