We are asked to determine the coordinates of a point that is equidistance to the point (4, -6) and the origin. To do that we need first to determine the distance of this point to the origin using the following formula:
[tex]d=\sqrt[]{(x-x_0)^2+(y-y_0)^2_{}}[/tex]
Since the origin has coordiante (0, 0), this means:
[tex](x_0,y_0)=(0,0)[/tex]
Replacing:
[tex]d=\sqrt[]{(x)^2+(y)^2_{}}[/tex]
Now, replacing the point we get:
[tex]d=\sqrt[]{(4)^2+(-6)^2_{}}[/tex]
Solving the operations we get:
