Question

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

Answer 1

Answer:

|SQ|=5

Step-by-step 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