LEARN · EXPLAIN · REVISE

Find the x-coordinate of the centroid.

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 6.4 · PDF 45 / printed page 38

TOPIC 01

Applications of plane vectors

Build understanding of applications of plane vectors through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

A=(0,0),\quad B=(9,0),\quad C=(0,3)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometry or physical quantity into vectors and check angle conventions.

Hint 2

Average the three vertex position vectors.

Worked solution

Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$G=(A+B+C)/3=(3,1)$
The centroid lies two-thirds along each median from the vertex.

The requested value is 3.

Checks and common pitfalls: The centroid lies two-thirds along each median from the vertex.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Connect geometric and algebraic forms of applications of plane vectors.
Geometry: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Physical quantities: Add forces as vectors; calculate work with a dot product.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Expected reasoning: Add forces as vectors; calculate work with a dot product.
Expected correction: An SSA triangle may have two valid configurations.