https://file.aiquickdraw.com/mathbot/file/1730335692444mr6pcgty.jpg

In this triangle \( \triangle MNO \), point \( S \) is the centroid, which is the intersection point of the three medians \( MP \), \( NQ \), and \( OR \). A centroid divides each median into a ratio of \( 2:1 \), with the longer segment being from the vertex to the centroid.

Since we are given that \( SQ = 2 \), this is the shorter segment (the part from \( S \) to \( Q \)). In a \( 2:1 \) ratio, the length of the segment from \( S \) to the opposite vertex (in this case, \( M \) through \( S \) to \( Q \)) would make \( MS \) twice as long as \( SQ \).

Therefore:
\[
MS = 2 \times SQ = 2 \times 2 = 4
\]

So, the answer is:
\[
MS = 4
\]

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### Related Questions
1. What is the significance of a centroid in a triangle?
2. How does a centroid divide each median of a triangle?
3. Can you find \( NS \) if \( SP = 3 \)?
4. How would the solution change if \( S \) was not the centroid?
5. How are medians related to the area of a triangle?

### Tip
Remember that in any triangle, the centroid divides each median in a \( 2:1 \) ratio, with the longer segment always being from the vertex to the centroid.

In triangle MNO, S is the intersection of the three medians. If SQ = 2, find MS.

Solve for MS in triangle MNO where S is the centroid and divides each median in a 2:1 ratio. Given SQ = 2, calculate MS using centroid properties.

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