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Question

The in-centre of a triangle with vertices (1,3), (0,0), and (2,0) is


A

1,13

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B

1,23

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C

1,32

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D

None of these

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Solution

The correct option is A

1,13


Step 1: Using distance formula, find the lengths of the sides of the triangle

Let A(1,3), B(0,0), and C(2,0) be the vertices of the triangle.

Using distance formula,

AB=1-02+3-02

=2 ...(i)

BC=0-22+0-02

=2 ...(ii)

AC=1-22+3-02

=2 ...(iii)

Step 2: Deduce the type of the triangle

From (i),(ii),(iii) we get that

AB=AC=BC

ABC is an equilateral triangle

In an equilateral triangle, the centroid and in-centre are coincident.

Step 3: Use formula for centroid of the triangle

The centroid of the triangle is given as

G=xA+xB+xC3,yA+yB+yC3

=1+0+23,3+0+03

G=1,13

Hence, the in-centre of the triangle is 1,13, so, option A is the correct answer.


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