Which point on the y-axis is equidistant from the points (12, 3) and (-5, 10)?

Let the required point on the y-axis (0, y).

Given (0, y) is equidistant from (12, 3) and (-5, 10).

Therefore, 

distance between (0, y) and (12, 3) = distance between (0, y) and (-5, 10)

To find the distance between two points , we can use distance formula:

d =  $\sqrt{({\mathrm{x}}_2-{\mathrm{x}}_1{)}^{2 }+{({\mathrm{y}}_2-{\mathrm{y}}_1)}^2 }$

 $\Rightarrow \sqrt{{\left(12-0\right)}^2+{\left(3-\mathrm{y}\right)}^2}=\sqrt{{\left(-5-0\right)}^2+{\left(10-\mathrm{y}\right)}^2}$

Squaring on both side,

$\Rightarrow 144+9+{\mathrm{y}}^2-6\mathrm{y}=25+100+{\mathrm{y}}^2-20\mathrm{y}$

$\Rightarrow -6y + 20y = 125 - 153 + y^2-y^2$

$\Rightarrow 14y = -28$

$\Rightarrow y = -2$

Therefore, the required point on the y-axis is (0, -2).