Question:
The point on the line \(y = x\) equidistant from \((4,0)\) and \((5,1)\) is
The point on the line \(y = x\) equidistant from \((4,0)\) and \((5,1)\) is
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Use symmetry when point lies on line \(y=x\).
Updated On: Apr 18, 2026
- (2,2)
- (3,3)
- \((5/2,5/2)\)
- \((1/2,1/2)\)
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The Correct Option is C
Solution and Explanation
Concept:
Equidistant $\Rightarrow$ distances equal.
Step 1: Let point.
\[ (x,x) \]
Step 2: Apply distance formula.
\[ (x-4)^2 + (x-0)^2 = (x-5)^2 + (x-1)^2 \]
Step 3: Simplify.
\[ x^2 -8x +16 + x^2 = x^2 -10x +25 + x^2 -2x +1 \] \[ 2x^2 -8x +16 = 2x^2 -12x +26 \] \[ 4x = 10 \Rightarrow x=\frac{5}{2} \]
Step 1: Let point.
\[ (x,x) \]
Step 2: Apply distance formula.
\[ (x-4)^2 + (x-0)^2 = (x-5)^2 + (x-1)^2 \]
Step 3: Simplify.
\[ x^2 -8x +16 + x^2 = x^2 -10x +25 + x^2 -2x +1 \] \[ 2x^2 -8x +16 = 2x^2 -12x +26 \] \[ 4x = 10 \Rightarrow x=\frac{5}{2} \]
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