- A(4, -4)
- B(2, -2)
- C(0, -3)
- D(5, -1)
Step-by-Step Solution
Centroid → → . Centroid → → . Third vertex = (4, −4).
Answer: A) (4, -4)
Two vertices of a triangle are (3, 2) and (−2, 1). Its centroid is . Find the third vertex.
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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