The centroid of a triangle is the intersection of at least two medians in a triangle. The orthocenter is the intersection of at least two altitudes in a triangle.
To find the centroid we have to draw at least two medians of the triangle, which is the segment between a vertex and the midpoint of the vertex's opposite side. Since the perpendicular bisector of a segment goes through its midpoint, we should find the perpendicular bisectors of two sides.
Finding perpendicular bisectors
Let's find the perpendicular bisector for RS. Open up a compass so that its width is greater than half the distance of RS, and draw two intersecting arcs using R and S as centers.
The line that contains both points of intersection is the perpendicular bisector to RS.
Let's repeat the process for RT.
Finding the Cntroid
By drawing segments from T and S to the midpoint of their opposite sides, we can locate the centroid at the intersection of these segments.
Orthocenter
To find the orthocenter we have to draw at least two altitudes of the triangle, which is the perpendicular segment from a vertex of the triangle to the line containing the opposite side.
Finding Perpendicular Lines
To find the line through T that is perpendicular to RS, open up a compass so that its width is greater than the distance between T and RS, and draw an arc that intersects this side at two points.
Next, using the arcs intersection with RS, draw a pair of intersecting arcs below T.
The ray that contains both T and the arc's intersection is perpendicular to RS.
Let's repeat the process for TS. Note that in order to do this, we have to extend TS somewhat.
Finding the Orthocenter
The orthocenter is the point of intersection of the altitudes drawn from T and R. Notice that this requires us to extend the altitude drawn from T.
