Question

find the point on Y- axis which is equidistant from A(6,5) and B (2,3)​

Answer 1

Answer:

(4,4)

Step-by-step explanation:

((x1+x2)/2,(y1+y2)/2)

((6+2)/2,(5+3)/2)

(4,4)

Answer 2

Step-by-step explanation:

The point is on the y-axis and hence the coordinates of that point are (0,y)

The distance between point A & (0,y) and B & (0,y) are equal.

Distance between any two point call the Distance formula is :

$d = \sqrt{(x _{2} - x _{1})^{2} - (y _{2} - y _{1})^{2} }$

$d = \sqrt{(6 - 0)^{2} + (5 - y)^{2} } \\ d = \sqrt{(2 - 0)^{2} + (3 - y)^{2} } \\ \sqrt{(6 - 0)^{2} + (5 - y)^{2} } = \sqrt{(2 - 0)^{2} + (3 - y)^{2} } \\ 36 + {(5 - y)}^{2} = 4 + {(3 - y)}^{2} \\ 32 + 25 + {y}^{2} - 10y = 9 + {y}^{2} - 6y \\ 57 - 10y = 9 - 6y \\ y = 12$

The point is (0,12)