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Question

If A (3, y) is equidistant from points P (8, -3) and Q (7, 6), find the value of y and find the distance AQ.

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Solution

A (3,y) P (8,-3) Q (7,6)
AP= AQ (given)
APblank squared=AQblank squared
left parenthesis 3 minus 8 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared space equals space left parenthesis 3 minus 7 right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared 25 space plus space y squared plus 9 plus 6 y space equals space 16 space plus space y squared thin space plus 36 minus 12 y 34 plus 6 y space equals space 52 minus 12 y 18 y equals 18 y equals 1

AQ = square root of left parenthesis 3 minus 7 right parenthesis squared plus left parenthesis 1 minus 6 right parenthesis squared end root equals square root of 16 plus 25 end root equals square root of 41 units

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