If the point (x, y) is equidistant from the points (7, 1) and (3, 5), then which one of the following options is correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x-y=2\)
By the distance formula, the distance of (x, y) from A(7, 1) is set equal to its distance from B(3, 5); squaring both removes the square roots.
\((x-7)^2+(y-1)^2=(x-3)^2+(y-5)^2\)
\(x^2-14x+49+y^2-2y+1=x^2-6x+9+y^2-10y+25\)
The \(x^2\) and \(y^2\) terms cancel: \(-14x-2y+50=-6x-10y+34\)
\(-8x+8y=-16\)
\(x-y=2\)