In Delta TUV Z is the centroid. If UZ=18 find ZY . Answer Attemptiout of 2 ZY=

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In Delta TUV Z is the centroid. If UZ=18 find ZY . Answer Attemptiout of 2 ZY=

Answer 1

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 \(Z\) is the centroid of \(\triangle TUV\), and \(UZ = 18\), we can use the property of the centroid to find \(ZY\).The median from vertex \(U\) to the midpoint of the opposite side (which is part of side \(VW\)) is divided by the centroid \(Z\) into two segments: \(UZ\) and \(ZY\). Since \(UZ\) is twice as long as \(ZY\), we can express this relationship as:\[UZ = 2 \cdot ZY\]We are given that \(UZ = 18\), so we can set up the equation:\[18 = 2 \cdot ZY\]Now, we solve for \(ZY\):\[ZY = \frac{18}{2}\]\[ZY = 9\]Therefore, the length of \(ZY\) is 9 units.

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In Delta TUV Z is the centroid. If UZ=18 find ZY . Answer Attemptiout of 2 ZY=

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