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Question
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
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Solution
Let C(x, 0) be a point on the x-axis, which is equidistant from the points A(7, 6) and B(3, 4).
\[\therefore\] AC = BC
\[\Rightarrow A C^2 = B C^2\]
\[\Rightarrow \left( 7 - x \right)^2 + \left( 6 - 0 \right)^2 = \left( 3 - x \right)^2 + \left( 4 - 0 \right)^2 \]
\[ \Rightarrow 49 + x^2 - 14x + 36 = 9 + x^2 - 6x + 16\]
\[ \Rightarrow 85 - 14x = 25 - 6x\]
\[ \Rightarrow 60 = 8x\]
\[ \Rightarrow \frac{15}{2} = x\]
Thus, the point on the x-axis, which is equidistant from the points (7, 6) and (3, 4) is \[\left( \frac{15}{2}, 0 \right)\]
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