find the centroid of the triangle whose vertices are (2, -3), (-4, 2)and(8, 13).
Answers
Given : A triangle with vertex (2, -3), (-4, 2)and(8, 13).
To Find : centroid of the triangle
Solution:
Centroid of triangle is given by :
( x₁ + x₂ + x₃)/3 , ( y₁+ y₂ + y₃)/3
where (x₁ , y₁) , ( x₂ , y₂) and ( x₃ , y₃) are the vertex of triangle
Here given vertex are (2, -3), (-4, 2)and(8, 13).
so centroid is ( 2 - 4 + 8)/3 , ( -3 + 2 + 13)/3
= ( 6/3) , (12/3)
= 2 , 4
2 ,4 is the centroid of triangle
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Given :-
- Vertices of triangle are (2, -3), (-4, 2)and(8, 13).
To Find :-
- Coordinates of the centroid of the triangle ?
Solution :-
we know that, if coordinates of vertices of ∆ are (x1,y1) , (x2,y2) and (x3,y3) then,
- Coordinates of centroid of ∆ (x,y) = (x1 + x2 + x3)/3 and (y1 + y2 + y3)/3 .
given that,
- x1 = 2
- y1 = - 3
- x2 = - 4
- y2 = 2
- x3 = 8
- y3 = 13 .
putting values we get,
→ x = {2 + (-4) + 8} / 3 = (10 - 4)/3 = 6/3 = 2 .
→ y = {(-3) + 2 + 13} / 3 = (15 - 3)/3 = 12/3 = 4.
hence, the coordinates of the centroid of the triangle are (2,4) .
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