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Byju's Answer
Standard X
Mathematics
Distance Formula
If the point ...
Question

If the point C(-2, 3) is equidistant from the points A(3, -1) and B(x, 8), find the values of x. Also, find the distance BC.

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Solution

f i n d i n g space d i s tan c e space b divided by w space p o i n t space A C square root of open parentheses 3 minus left parenthesis negative 2 right parenthesis close parentheses squared plus open parentheses negative 1 minus 3 close parentheses squared end root

equals square root of 25 plus 16 end root equals square root of 41
given distance AC=distance BC
square root of open parentheses negative 2 minus x close parentheses squared plus open parentheses 3 minus 8 close parentheses squared end root equals square root of 41 s q u a r i n g space b o t h space s i d e s space left parenthesis x plus 2 right parenthesis squared plus 25 equals 41 open parentheses x plus 2 close parentheses squared equals 16 t a k i n g space u n d e r r o o t space b o t h space s i d e s space w i l l space g i v e space 2 space c a s e s c a s e space 1 colon x plus 2 equals 4 x equals 2 c a s e space 2 colon x plus 2 equals negative 4 x equals negative 6

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