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Question
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Solution
Let (a, 0) be the point on the x axis that is equidistant from the points (7, 6) and (3, 4).
Accordingly, `sqrt((7 - a)^2 + (6 - 0)^2) = sqrt((3 - a)^2 + (4 - 0)^2)`
= `sqrt(49 + a^2 - 14a + 36) = sqrt(9 + a^2 - 6a + 16)`
= `sqrt(a^2 - 14a + 85) = sqrt(a^2 - 6a + 25)`
On squaring both sides, we obtain
a2 - 14a + 85 = a2 - 6a + 25
= -14a + 6a = 25 - 85
= -8a = -60
= `a = 60/8 = 15/2`
Thus, the required point on the x-axis is `(15/2, 0)`.
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