SME
Grade 10 Math · Problem type
Medians and the centroid
Use this for “The median AD is 12. How long are AG and GD?”
Diagram
AG = 8
AD = 12
This is an example. Type your own values to start a new problem.
AG
=
2
3
×
AD
GD
GD
calculated
Formulas
AG
=
2
×
AD
3
8
=
2
×
12
3
GD
=
AD
3
4
=
12
3
Assumptions
•
A median joins a corner to the midpoint of the opposite side.
•
The three medians meet at the centroid G, two thirds of the way from each corner.
•
So AG = 2/3 of AD and GD = 1/3 of AD: AG is twice GD.
•
Lengths are in any one unit.
Step-by-step
WE KNOW
AD = 12
FIND
AG (AG), GD (GD)
Step 1 · Find AG (AG)
Use AG = 2 × AD ÷ 3
The centroid is two thirds of the way from the corner.
AG
=
2
×
12
3
AG
=
24
3
AG = 8
Step 2 · Find GD (GD)
Use GD = AD ÷ 3
The last third of the median.
GD
=
12
3
GD = 4
Check
Put the numbers back in. Both sides should match.
8
=
2
×
12
3
✓
4
=
12
3
✓
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