Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Use the two-to-one division of a triangle's medians.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A median from vertex A to midpoint M has length 12 cm. Where does the centroid G lie along it?
Why this math matters
Connect the geometric balance point of a uniform triangular lamina with coordinate averages. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Locate the centroid along a median
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A median from vertex A to midpoint M has length 12 cm. Where does the centroid G lie along it?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
AG:GM=2:1
The centroid is nearer the midpoint than the vertex.
Develop the calculation
12 cm ÷ 3 = 4 cm per ratio part
The complete median consists of three such parts.
Check and interpret
AG=8 cm; GM=4 cm
The longer segment is the one adjacent to the vertex.
The result
AG=8 cm; GM=4 cm
The longer segment is the one adjacent to the vertex.
Common mistakes to catch
- The ratio starts at the vertex, not at the side midpoint.
- A median joins a vertex to the midpoint of the opposite side.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
If AG=10 cm, what is the full median AM?
Show a hint
AG is two thirds of the whole median.
Reveal answer and explanation
15 cm
10 ÷ (2/3)=15.
Practice 2
For vertices (0,0),(6,0),(0,9), what are the centroid coordinates?
Show a hint
Average the three x values and the three y values.
Reveal answer and explanation
(2,3)
(0+6+0)/3=2 and (0+0+9)/3=3.
Take the idea with you
Connect the geometric balance point of a uniform triangular lamina with coordinate averages.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Find points equally distant from two endpoints
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.