Question

Pond the coordinates of the point on x-axis which is equidistant from the
points (-2,5) and (2,-3).
(CBSE 2017)​

Answer 1

Answer:

Let the given points be A( -2 , 5 ) and B( 2 , -3 ) .

And, let the required point on x-axis be P( x , 0 ) .

Then,

→ PA = PB . [ A and B are equidistant from P ]

[ Squaring both side ]

=> PA² = PB² .

[ Using distance formula ]

=> [ x - ( -2 ) ]² + ( x - 5 )² = ( x - 2 )² + [ 0 - ( -3 ) ]² .

=> ( x + 2 )² + ( 0 - 5 )² = ( x - 2 )² + ( 0 + 3 )² .

=> ( x + 2 )² + 25 = ( x - 2 )² + 9 .

=> ( x + 2 )² - ( x - 2 )² = 9 - 25 .

=> [ ( x + 2 ) + ( x - 2 ) ] [ ( x + 2 ) - ( x - 2 ) ] = - 16 .

=> ( x + 2 + x - 2 ) ( x + 2 - x + 2 ) = - 16 .

=> ( 2x ) ( 4 ) = - 16 .

=> 8x = - 16 .

=> x = -16/8 .

•°• x = -2 .

hope it helps you

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Answer 2

Answer:

Step-by-step explanation: