Question

If the midpoints of the sides ofa triangle are (-2, 3), (4, -3), (4, 5), find its vertices. 

Answer 1

Let P(x₁, y₁), Q(x₂, y₂ ) and  R(x₃, y₃) be the coordinates of the vertices of .Δ PQR

Midpoint of PQ is D 

D (-2 , 3) = D `(("x"_1 + "x"_2)/2 , ("y"_1 + "y"_2)/2)`

`("x"_1 + "x"_2)/2 = - 2   ,  ("y"_1 + "y"_2)/2 = 3`

X₁ + X₂ = -4   .....(1),        Y₁ + y₂ = 6 .......(2)

similarly, 

X₂ + X₃ = 8  ......(3),    y₂ + y₃ = -6    ....(4)

X₁+ X ₃ = 8    ....(5),   y₁ +y₃ = 10  ......(6) 

Adding (1), (3) and (5) 

2(x₁ + x₂ + x₃ ) = 12 

x₁ + x₂ + x₃  = 6

- 4 + x₃ = 6

x₃ = 10

Adding (2), ( 4) and (6) 

2(Y₁+ Y₂ + Y₃) =  10

Y₁+ Y₂ + Y₃  = 5

6 + Y₃ = 5

Y₃ = -1