.If two vertices of a triangle are (0, -2) and (-3, 1) and
the centroid is at the origin, then third vertex is
Answers
Answer :-
(3, 1)
Given :-
- Centroid of the triangle is origin
- Two vertices of triangle are (0, -2 ) , (-3 , 1)
To find :-
- Third vertex
Solution:-
As we know that centroid of the triangle is
G = ( x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃/3)
According to the Question,
- (x₁ , y₁ ) = (0, -2)
- (x₂, y₂) = (-3, 1)
- (x₃, y₃) = (x, y)
- G = (0,0) [ origin ]
Substituting the values ,
(0,0) = ( 0 -3 +x/3 , -2 + 1 + y/3)
(0,0) = (x-3/3 , y-1/3)
Equating the co-ordinates
x -3/3 =0
x-3 =0(3)
x - 3 = 0
x = 3
y- 1 /3 =0
y-1 = 3(0)
y - 1 = 0
y = 1
So, (x,y) = (3,1)
So, the third vertex of a triangle is (3,1)
Verification:-
As we got here the three vertices Since, these three vertices Centroid must be(0,0)
G = ( x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃/3)
- (x₁ , y₁ ) = (0, -2)
- (x₂, y₂) = (-3, 1)
- (x₃, y₃) = (3, 1)
Substituting the values,
(0,0) = ( 0 -3 + 3/3 , -2 +1+ 1/3)
(0,0) = (0/3 , -2+2/3)
(0,0) = (0,0/3)
(0,0) = (0,0)
Hence verified !
Answer :-
(3, 1)
Given :-
Centroid of the triangle is origin
Two vertices of triangle are (0, -2 ) , (-3 , 1)
To find :-
Third vertex
Solution:-
As we know that centroid of the triangle is
G = ( x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃/3)
According to the Question,
(x₁ , y₁ ) = (0, -2)
(x₂, y₂) = (-3, 1)
(x₃, y₃) = (x, y)
G = (0,0) [ origin ]
Substituting the values ,
(0,0) = ( 0 -3 +x/3 , -2 + 1 + y/3)
(0,0) = (x-3/3 , y-1/3)
Equating the co-ordinates
x -3/3 =0
x-3 =0(3)
x - 3 = 0
x = 3
y- 1 /3 =0
y-1 = 3(0)
y - 1 = 0
y = 1
So, (x,y) = (3,1)
So, the third vertex of a triangle is (3,1)
Verification:-
As we got here the three vertices Since, these three vertices Centroid must be(0,0)
G = ( x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃/3)
(x₁ , y₁ ) = (0, -2)
(x₂, y₂) = (-3, 1)
(x₃, y₃) = (3, 1)
Substituting the values,
(0,0) = ( 0 -3 + 3/3 , -2 +1+ 1/3)
(0,0) = (0/3 , -2+2/3)
(0,0) = (0,0/3)
(0,0) = (0,0)
Hence verified !