- A(1, 2)
- B(1.5, 3)
- C(2, 1)
- D(3, 6)
Step-by-Step Solution
Centroid = . Dividing the two sums by 2 instead of 3 gives (1.5, 3); leaving out the division altogether gives (3, 6), which is just the pair of sums.
Answer: A) (1, 2)
A triangular park has corners at P(−6, 2), Q(4, −4) and R(5, 8). A fountain is to be built at the centroid of the triangle. Find its coordinates.
Class 10Coordinate GeometryGeometry — Coordinates
Key idea: Centroid of a triangle
The **centroid** is the point where the three medians of a triangle meet (a median connects a vertex to the midpoint of the opposite side). It is the 'balance point' of the triangle.
**Coordinates**: just the average of the three vertices:
.
**Example**: Triangle with A(0, 0), B(6, 0), C(3, 9).
Centroid: = (3, 3).
A useful invariant — the centroid divides each median in ratio 2:1 from the vertex.
**Coordinates**: just the average of the three vertices:
.
**Example**: Triangle with A(0, 0), B(6, 0), C(3, 9).
Centroid: = (3, 3).
A useful invariant — the centroid divides each median in ratio 2:1 from the vertex.
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