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 (

*x*_{1},*y*_{1}), (*x*_{2},*y*_{2}) and (*x*_{3},*y*_{3}) respectively. Let P (3, 4), Q (4, 1) and R (2, 0) be the mid parts of sides BC, AC and AB respectivelyAdding equations (1), (3) and (5)

2 (

*x*_{1}+*x*_{2}+*x*_{3}) = 18⇒

*x*_{1}+*x*_{2}+*x*_{3 }= 9 … (7)Subtracting equation (1), (3) and (5) from equation (7), it is obtained

*x*

_{1}= 9 – 6 = 3

*x*

_{2}= 9 – 8 = 1

*x*

_{3 }= 9 – 4 = 5

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

2 (

*y*_{1}+*y*_{2}+*y*_{3}) = 10⇒

*y*_{1}+*y*_{2}+*y*_{3}= 5 … (8)Subtracting equation (2), (4) and (6) from equation (8), it is obtained

*y*

_{1}= 5 – 8 = –3

*y*

_{2}= 5 – 2 = 3

*y*

_{3 }= 5 – 0 = 5

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

Hope! This will help you.

Cheers!

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