A point on the y-axis which is equidistant from the points A(6, 5) and B(−4, 3) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (0, 9)
Every point on the y-axis has x-coordinate 0, so let the point be \(P(0,y)\). Being equidistant from A and B, it has equal distances to both; squaring the distance formula removes the roots.
\(PA^2=(6-0)^2+(5-y)^2=36+(5-y)^2\)
\(PB^2=(-4-0)^2+(3-y)^2=16+(3-y)^2\)
Setting \(PA^2=PB^2\): \(36+25-10y+y^2=16+9-6y+y^2\)
\(61-10y=25-6y\), so \(4y=36\) and \(y=9\)