Question

The co-ordinates of the point on y-axis which is equidistant from the points A(3, 1) and B(1, 5) is:

• A. (2,0)
• B. (4,0)
• C. (0,4)
• D. (0,2)

Answer 1

The correct option is D

(0,2)

Any point on the y-axis is of the form C (0,y)

$AC=BC\Rightarrow A{C}^2=B{C}^2\Rightarrow 3^2+(y-1{)}^2=1^2+(y-5{)}^2\Rightarrow 9+y^2+1-2y=1+y^2+25-10y\Rightarrow 9-2y=25-10y\Rightarrow 8y=16\Rightarrow y=2$

Hence, the required point is C(0,2)