Question

Find the coordinates of the point on the y-axis which is equidistant from the points a(5, 3) and b(1, –5).

Answer 1

This is the correct answer
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Answer 2

Answer:  P(0,y) = $(0,\frac{1}{2})$ on the y-axis which is equidistant from the A and B.

Step-by-step explanation:

Since we have given that

Let the point on y-axis say P(0,y) is equidistant from the points A(5,3) and B(1,-5).

So, we will apply the "Distance formula":

$PA=PB\\\\PA^2=PB^2\\\\5^2+(3-y)^2=1^2+(-5-y)^2\\\\25+9-6y+y^2=1+25+y^2+10y\\\\34-6y=26+10y\\\\34-26=10y+6y\\\\8=16y\\\\y=\frac{8}{16}=\frac{1}{2}$

Hence, P(0,y) is given by

$(0,\frac{1}{2})$ on the y-axis which is equidistant from the A and B.