The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___

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The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___

Options:

A . (0, 15)

B . (0, 14)

C . (0, 13)

D . (15 , 0)

Answer: Option A
:
A

$Any point on the y-axis has coordinates of the form (0, y) . Since the point is equidistant from both points (- 3, 4) and (7, 6) by distance formula, 3^{2} + {(y - 4)}^{2} = 7^{2} + {(y - 6)}^{2} 16 - 8 y = 40 + 36 - 12 y 4 y = 60 y = 15 ∴ the point is (0, 15) .$

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