Question

Given that S is the centroid of triangle MNO, find SQ.

Answer 1

|SQ|=5

Explanation:

If S is the median, then OP is a median of triangle OMN.

This implies that:

|MP|=|NP|

`3x-4=x+4`

We group like terms and solve for x.

`3x-x=4+4`

`\implies 2x=8`

`\implies x=4`

Now we know that: MN:SQ=2:1

But MN=2x+2

This implies that:

2x+2:SQ=2:1

Put x=4

2(4)+2:SQ=2:1

10:SQ=2:1

Therefore |SQ|=5