Question

Determine the coordinates of the vertices of a triangle if the middle points
of its sides have the coordinates (2, -3), (4, 2) and (-5,-2).
​

Answer 1

Answers :-

• A = (-7 , -7)
• B = (11, 1)
• C = (-3 , 3)

Concept Implemented:-

If ( x₁ , y₁ ) , (x₂ , y₂ ) , (x₃, y₃) are the mid points of the triangle then the required vertices are

A = ( x₁ + x₃ - x₂ , y₁ + y₃ - y₂ )

B = ( x₁ + x₂ - x₃ , y₁ + y₂ - y₃)

C = (x₂ + x₃ - x₁ , y₂ + y₃ - y₁)

Trick :-

The opposite vertices should be subtract from the sum of remaining vertices

If we substitute the values then we can get the co-ordinates of the vertices of the Triangle

SOLUTION :-

So, According to the Question

( x₁ , y₁ ) = (2 , -3)

(x₂ , y₂ ) = (4 , 2)

(x₃, y₃) = ( - 5 , -2 )

Substituting the values ,

A = ( x₁ + x₃ - x₂ , y₁ + y₃ - y₂ )

A = ( 2 -5 - 4 , -3-2 -2 )

A = ( 2- 9 , -7)

A = (-7 , -7)

So, the co-ordinates of A are (-7 , -10)

Similarly finding the co-ordinates of B and C

B = ( x₁ + x₂ - x₃ , y₁ + y₂ - y₃)

B = ( 2 +4 -[-5] , -3 +2 -[-2] )

B = ( 2+4 +5 , -3 +2 +2)

B = ( 11 , 1 )

So, the co-ordinates of B are (11 , 1)

C = (x₂ + x₃ - x₁ , y₂ + y₃ - y₁)

C = ( 4 - 5 -2 , 2-2 -[-3] )

C = ( 4-7 , +3)

C = (-3 , 3)

So, the co-ordinates of C are (-3,3)