Question:
Let \(A(7,2)\), \(B(0,1)\) be any two points. If the distance of \(P(x,5)\) from \(A\) is same as the distance from \(B\), then the value of \(x\) is
Let \(A(7,2)\), \(B(0,1)\) be any two points. If the distance of \(P(x,5)\) from \(A\) is same as the distance from \(B\), then the value of \(x\) is
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When two distances are equal, square both sides to remove roots quickly.
Updated On: Jul 15, 2026
- \(2\)
- \(3\)
- \(4\)
- \(5\)
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The Correct Option is B
Solution and Explanation
Given:
\[
PA=PB
\]
Using distance formula:
\[
\sqrt{(x-7)^2+(5-2)^2}=\sqrt{(x-0)^2+(5-1)^2}
\]
Squaring:
\[
(x-7)^2+9=x^2+16
\]
Expand:
\[
x^2-14x+49+9=x^2+16
\]
Simplify:
\[
-14x+58=16
\Rightarrow -14x=-42
\Rightarrow x=3
\]
Thus,
\[
\boxed{3}
\]
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