Where is the centre of gravity of a scalene triangle located?

Question

Examoogle · Accepted Answer

The correct answer is Option B: The intersection of its medians. Remember the mnemonic 'Centroid = Median intersection'. The centroid divides each median in a 2:1 ratio from the vertex to the midpoint of the opposite side.

Step-by-Step Solution & Concepts:
Shortcut Trick: Remember the mnemonic 'Centroid = Median intersection'. The centroid divides each median in a 2:1 ratio from the vertex to the midpoint of the opposite side.

Formula Used: $$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$$

Given: The question asks for the definition of the center of gravity (centroid) of a scalene triangle.

Steps: Define the Center of Gravity: In geometry, the center of gravity of a triangle is known as the centroid. It is the point where the three medians of the triangle intersect.. Coordinate Geometry Representation: If the vertices of a scalene triangle are $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$, the coordinates of the centroid are given by the average of the coordinates.. Verify with Options: Option B states 'The intersection of its medians', which matches the geometric definition of the centroid (center of gravity).

Answer: B is correct because the center of gravity, or centroid, is mathematically defined as the intersection point of the three medians of a triangle.

Exam Tip: The centroid always divides each median in the ratio 2:1, which is a frequent concept used in coordinate geometry problems involving triangle properties.

Examoogle · Answer

Option A: The midpoint of the base

Examoogle · Answer

Option C: The intersection of its altitudes

Examoogle · Answer

Option D: The midpoint of one of the sides

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