alleryA point on the $y$-axis is equidistant from $A(6,5)$ and $B(-4,3)$. What is that point?
A$(0,5)$
B$(0,7)$
C$(0,9)$
D$(9,0)$
Answer & Solution
Correct answer: C. $(0,9)$
A point on the $y$-axis has coordinates $(0,y)$.
Equating distances from $(0,y)$ to $A$ and $B$ gives $(6-0)^2+(5-y)^2=(-4-0)^2+(3-y)^2$, which simplifies to $y=9$.
**So the point is $(0,9)$.**
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