Question

find the point on the y-axis which is equidistant from (5,9) and ( -4,6) ​

Answer 1

Answer:

(0,9)

Step-by-step explanation:

Let the point be (0,y).

From the question,

$\sqrt{( {5}^{2}) + ( {y - 9}^{2} ) } = \sqrt{( { (- 4)}^{2}) + {(y - 6)}^{2} } \\ 25 + {(y - 9)}^{2} = 16 + {(y - 6)}^{2} \\ 9 = {y}^{2} - 12y + 36 - ( {y}^{2} - 18y + 81) \\ 9 = 18y - 12y + 36 - 81 \\ 9 = 6y - 45 \\ 6y = 54 \\ y = 9$

So the point is (0,9).

Thank you