Question
In Delta TUV Z is the centroid. If UZ=18 find ZY . Answer Attemptiout of 2 ZY=
Answer
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Jocelyn
Professional · Tutor for 6 years
Answer
To solve this problem, we need to understand the properties of a centroid in a triangle. The centroid of a triangle is the point where the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid has a special property: it divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment from the centroid to the midpoint of the side.Given that
is the centroid of
, and
, we can use the property of the centroid to find
.The median from vertex
to the midpoint of the opposite side (which is part of side
) is divided by the centroid
into two segments:
and
. Since
is twice as long as
, we can express this relationship as:
We are given that
, so we can set up the equation:
Now, we solve for
:
Therefore, the length of
is 9 units.