Question

if coordinates of two vertices of a triangle are (1,-1) and (-4,2) and the centroid is (0,2), then the coordinates of the third vertex are​

Answer 1

Answer:

The coordinates of third vertex is (3, 5)

Step-by-step explanation:

we know that

x co-ordinate of centroid = (x1 + x2 + x3)/3

=> 0 = ( 1 -4 + x)/3

=> 0 = ( -3 + x)

=> x = 3

also

y co-ordinate of centroid = (y1 + y2 + y3)/3

=> 2 = ( -1 +2 + y)/3

=> 6 = ( 1 + y )

=> y = 5

Answer 2

Given :- if coordinates of two vertices of a triangle are (1,-1) and (-4,2) and the centroid is (0,2) .

To Find :- The coordinates of the third vertex ?

Formula used :- if (x₁ , y₁) , ( x₂ , y₂) and ( x₃ , y₃) are the vertex of a triangle then, centroid of the triangle is given by :-

• x = (x₁ + x₂ + x₃) / 3
• y = (y₁+ y₂ + y₃) / 3

Solution :-

Let us assume that, the coordinates of the third vertex are (x, y) .

given that,

• x₁ = 1
• y₁ = - 1
• x₂ = - 4
• y₂ = 2
• x₃ = x
• y₃ = y
• x = 0
• y = 2

So, putting given values in above told formula we get,

→ x = (x₁ + x₂ + x₃)/3

→ 0 = (1 - 4 + x)/3

→ 0 = x - 3

→ x = 3

and,

→ y = (y₁+ y₂ + y₃)/3

→ 2 = (-1 + 2 + y)/3

→ 6 = 1 + y

→ y = 6 - 1

→ y = 5

therefore, the coordinates of the third vertex are (3, 5) .

Learn more :-

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