Video Transcript
In triangle 𝐽𝐾𝐿, 𝐽𝑃 equals six
centimeters. Find the length of line segment
𝑃𝑆.
We need to know the length of line
segment 𝑃𝑆, and we’ve been given that 𝐽𝑃 equals six centimeters. First of all, we should note that
the point 𝑆 divides the line segment 𝐾𝐿 in half, which makes 𝑆 a midpoint. Since 𝐽 is a vertex of this
triangle, we know that the distance between a vertex and the midpoint is called the
median. And so we can say that 𝐽𝑆 is a
median. In the same way, 𝑇 divides line
segment 𝐽𝐿 and 𝑅 divides line segment 𝐽𝐾, which means 𝐾𝑇 is a median and 𝐿𝑅
is a median. Since 𝐽𝑆, 𝐾𝑇, and 𝐿𝑅 are all
meet at one point 𝑃, 𝑃 is the point of concurrency or the centroid.
This is important because we know
something about the centroid. For a median, the distance between
the vertex and the centroid is two-thirds of the median. And the distance between the
centroid and the midpoint is one-third of the distance of that median. To go from two-thirds to one-third,
we multiply by one-half. One-third is half of
two-thirds. And so we can say that the line
segment 𝑃𝑆 will be equal to one-half the line segment 𝐽𝑃. Since 𝐽𝑃 was equal to six
centimeters, we take one half of that and we say that the line segment 𝑃𝑆 is equal
to three centimeters.
