Using analytic geometry, find the coordinates of the point on the x ax

Pearl Carney 2021-11-20 Answered
Using analytic geometry, find the coordinates of the point on the x axis which is equidistant from \(\displaystyle{A}{\left({5},\ {8}\right)}\) and \(\displaystyle{B}{\left(-{3},\ {4}\right)}\)

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Expert Answer

Opeance1951
Answered 2021-11-21 Author has 651 answers

Step 1
Given, \(\displaystyle{A}{\left({5},\ {8}\right)},\ {B}{\left(-{3},\ {4}\right)}\)
Let, equidistent point, \(\displaystyle{p}{\left({x},\ {0}\right)}\)
So, using distance formula:
\(\displaystyle\sqrt{{{\left({x}-{5}\right)}^{{{2}}}+{\left({8}\right)}^{{{2}}}}}=\sqrt{{{\left({x}+{3}\right)}^{{{2}}}+{\left(-{4}\right)}^{{{2}}}}}\)
Both Side:
\(\displaystyle{{{x}^{{{2}}}}}+{25}-{10}{x}+{64}={{{x}^{{{2}}}}}+{9}+{6}{x}+{16}\)
\(\displaystyle{25}+{64}-{9}-{16}={10}{x}+{6}{x}\)
\(\displaystyle{16}{x}={64}\)
\(\displaystyle{x}={4}\)
Coordinate is \(\displaystyle{\left({4},\ {0}\right)}\)

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