the mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

Hi Adnan!

Here is the answer to your question.

 

Let the coordinates of vertices A, B and C of the ∆ABC be (x₁, y₁), (x₂, y₂) and (x₃, y₃) respectively. Let P (3, 4), Q (4, 1) and R (2, 0) be the mid parts of sides BC, AC and AB respectively

 

Adding equations (1), (3) and (5)

2 (x₁ + x₂ + x₃) = 18

⇒ x₁ + x₂ + x₃ = 9     … (7)

Subtracting equation (1), (3) and (5) from equation (7), it is obtained

x₁ = 9 – 6 = 3

 x₂ = 9 – 8 = 1

x₃ = 9 – 4 = 5

 

Adding equations (2), (4) and (6)

2 (y₁ + y₂ + y₃) = 10

⇒ y₁ + y₂ + y₃ = 5    … (8)

 

Subtracting equation (2), (4) and (6) from equation (8), it is obtained

y₁ = 5 – 8 = –3

 y₂ = 5 – 2 = 3

y₃ = 5 – 0 = 5

 

Thus, the vertices of the triangles are (3, –3), (1, 3) and (5, 5)

 

Hope! This will help you.

Cheers!