Chapter 10.8, Problem 6ST3

To determine

Find the locus of all the points that are equidistant from the vertices of $\Delta RST$ .

Answer to Problem 6ST3

The locus of all the points that are equidistant from the vertices of $\Delta RST$ is the line perpendicular to plane containing $\Delta RST$ , and passing through G.

Explanation of Solution

Given:

  $\Delta RST$ is isosceles triangle.

Calculation:

Construct the isosceles triangle :

  

G is the centroid of the $\Delta RST$ and is equidiatant from the vertices of the triangle.

Now , if we move G such than the distance of RG, SG , and TG remains constant, is only possible if G is moved on the perpendicular line passing through the plane containing $\Delta RST$ and passing through G.

So, the locus of all the points that are equidistant from the vertices of $\Delta RST$ is the line perpendicular to plane containing $\Delta RST$ , and passing through G.