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.
By distance formula
AC = √{(3 – (– 2))2 + (– 1 – 3)2}
= √{(5)2 + (– 4)2}
= √{25 + 16}
= √{41}
BC = √{(x –(– 2))2 + (8 – 3)2}
= √{(x + 2)2 + 52 }
= √{x2 + 4 + 2x + 25}
= √{x2 + 2x + 29}
AB = BC
√{x2 + 2x + 29} = √{41}
× = 2 or × = – 6
Since, AB = BC
BC = √41 units
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