Question

find the point on the y axis which is equidistant from the points A(6,5)and B( -4,3)

Answer 1

hope it helps. . . . . mark as brainliest answer

Answer 2

The point P(0,9) is equidistant from the points A(6,5) and B(-4,3).

Step-by-step explanation:

Let the point on y axis is P(0,y) which is equidistant from the points A(6,5) and B(-4,3). The distance between PA is equal to PB such that,

$PA=PB\\\\\tt \sqrt{\bigg(0\ -\ 6\bigg)^2\ +\ \bigg(y\ -\ 5\bigg)^2}\ =\ \sqrt{\bigg(0\ +\ 4\bigg)^2\ +\ \bigg(y\ -\ 3\bigg)^2}\\\\\\\\\sqrt{\bigg(-6\bigg)^2\ +\ y^2\ -\ 10y\ +\ 25}\ =\ \sqrt{\bigg(4\bigg)^2\ +\ y^2\ -\ 6y\ +\ 9}\\\\\\\\\sqrt{\bigg[36\ +\ y^2\ -\ 10y\ +\ 25\bigg]}\ =\ \sqrt{\bigg[16\ +\ y^2\ -\ 6y\ +\ 9\bigg]}$

On squaring,

$\tt 36\ +\ y^2\ -\ 10y\ +\ 25\ =\ 16\ +\ y^2\ -\ 6y\ +\ 9\\\\\\61\ -\ 10y\ =\ 25\ -\ 6y\\\\\\61\ -\ 25\ =\ -6y\ +\ 10y\\\\\\36\ =\ 4y\\\\\\y\ =\ 9$

So, the point P(0,9) is equidistant from the points A(6,5) and B(-4,3).

Learn more,

Distance formula

https://brainly.in/question/16161542