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Question

If the distance between (2,3) and (-5,2) is equal to the distance between (x,2) and (1,3), then the values ofx are


A

-6,8

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B

6,8

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C

-8,6

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D

-7,7

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Solution

The correct option is A

-6,8


Explanation for correct option

Given that the distance between (2,3) and (-5,2) is equal to the distance between (x,2) and (1,3)

We know that the distance between two points say x1,y1 and x2,y2 =x2-x12+y2-y12

Distance between (2,3) and (-5,2) = =(-5-2)2+(2-3)2=49+1=50

Distance between (x,2)and(1,3) =(1-x)2+(3-2)2=1-2x+x2+1=2-2x+x2

Since the distance are equal,

2-2x+x2=502-2x+x2=50x2-2x-48=0x2-8x+6x-48=0xx-8+6x-8=0x-8x+6=0x=-6,8

Hence option (A) is correct i.e. -6,8


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