find the value of x for which the distance between the points p[2,-3] & q[x,5] is 10 units.
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here is your answer OK ☺☺☺☺☺
By Distance Formula :-
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√ ( 2 - x )2 + ( - 3 - 5 )2 = 10
Squaring on both sides :-
4 + x2 - 4x + 64 = 100
x2 - 4x + 68 - 100 = 0
x2 - 4x - 32 = 0
x2 - 8x + 4x - 32 = 0
x ( x - 8 ) + 4 ( x - 8 ) = 0
( x + 4 ) ( x - 8 ) = 0
x = - 4 or 8
By Distance Formula :-
__________________
√ ( 2 - x )2 + ( - 3 - 5 )2 = 10
Squaring on both sides :-
4 + x2 - 4x + 64 = 100
x2 - 4x + 68 - 100 = 0
x2 - 4x - 32 = 0
x2 - 8x + 4x - 32 = 0
x ( x - 8 ) + 4 ( x - 8 ) = 0
( x + 4 ) ( x - 8 ) = 0
x = - 4 or 8
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