5.4. Medians http://www.ck12.org
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52530CK-12 Foundation: Chapter5MediansB
Concept Problem Revisited
The point that you should put the wire through is the centroid. That way, each triangle will balance on the wire.
The triangle that we wanted to plot on thex−yplane is to the right. Drawing all the medians, it looks like the
centroid is (8, 4). To verify this, you could find the equation of two medians and set them equal to each other and
solve forx. Two equations arey=^12 xandy=− 4 x+36. Setting them equal to each other, we find thatx=8 and
theny=4.
Vocabulary
Amedianis the line segment that joins a vertex and the midpoint of the opposite side in a triangle. Amidpointis
a point that divides a segment into two equal pieces. Acentroidis the point of intersection for the medians of a
triangle.
Guided Practice
- Find the equation of the median fromBto the midpoint ofACfor the triangle in thex−yplane below.