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UPSC NDA I 2016 Mathematics Solved Paper

Question Numbers: 27-28

Direction: For the next two (2) items that follow:

Consider the lines

y = 3x,y = 6x and y

= 9

Question : 28 of 120

Marks: +1, -0

The centroid of the triangle is at which one of the following points?

Solution:

Concept:

The centroid of a triangle is the point where its three medians intersect.

If vertices are

A(x_1,y_1)

B(x_2,y_2)

C(x_3,y_3)

, then the centroid is

\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)

Explanation:

Given vertices:

A(3,9)

B(0,0)

C\left(\frac{3}{2},9\right)

Apply centroid formula:

x

-coordinate:

\frac{3+0+\frac{3}{2}}{3} = \frac{3+\frac{3}{2}}{3} = \frac{\frac{9}{2}}{3} = \frac{3}{2}

y

-coordinate:

\frac{9+0+9}{3} = \frac{18}{3} = 6

Thus centroid is

\left(\frac{3}{2},6\right)

Answer:

Option B:

\left(\frac{3}{2},6\right)

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