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The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. What are the coordinates of the centroid of the triangle ABC

Solution:

Given, the vertices of ∆ ABC are A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃).

We have to find the centroid of the triangle ABC.

The centroid of a triangle is the point of intersection of the three medians of a triangle.

The formula for the centroid of the triangle is given by

C = (a + b + c)/3, (d + e + f)/3

Where, a, b, c are the x-coordinates of the vertices of the triangle

d, e, f are the y-coordinates of the vertices of the triangle.

The centroid of the triangle A(x₁, y₁), B (x₂, y₂) and C (x₃, y₃) is given as

C = [(x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3]

Therefore, the centroid of the triangle ABC is (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3.

✦ Try This: A (4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ABC. Find the centroid of the triangle ABC.

Given, the vertices of the triangle ABC are A(4, 2) B(6, 5) and C(1, 4).

We have to find the centroid of the triangle ABC.

The formula for the centroid of the triangle is given by

C = (a + b + c)/3, (d + e + f)/3

Here, (a, b) = (4, 2) (c, d) = (6, 5) and (e, f) = (1, 4)

Centroid, C = [(4 + 6 + 1)/3, (2 + 5 + 4)/3]

= [11/3, 11/3]

Therefore, the centroid of the triangle ABC is (11/3, 11/3).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.4 Problem 3(iv)

The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. What are the coordinates of the centroid of the triangle ABC

Summary:

The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. The coordinates of the centroid of the triangle ABC are (x₁+x₂+x₃)/3 and (y₁+y₂+y₃)/3

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