find the vertices of the traingle …

Let vertices of {tex} \triangle ABC{/tex} be A(x_1, y₁), B(x₂, y₂) and C(x₃, y₃)
By mid-points formula
{tex}\frac{{{x_2} + {x_3}}}{2} = 3 \Rightarrow {x_2} + {x_3} = 6{/tex} ...... (i)
{tex}\frac{{{y_2} + {y_3}}}{2} = 1 \Rightarrow {y_2} + {y_3} = 2{/tex} ...... (ii)
{tex}\frac{{{x_3} + {x_1}}}{2} = 5 \Rightarrow {x_3} + {x_1} = 10{/tex} ..... (iii)
{tex}\frac{{{y_3} + {y_1}}}{2} = 6 \Rightarrow {y_1} + {y_3} = 12{/tex} ..... (iv)
{tex}\frac{{{x_1} + {x_2}}}{2} = - 3 \Rightarrow {x_1} + {x_2} = - 6{/tex} ..... (v)
{tex}\frac{{{y_1} + {y_2}}}{2} = 2 \Rightarrow {y_1} + {y_2} = 4{/tex} ...... (vi)
Adding (i), (iii) and (v)
 
2(x₁ + x₂ + x₃) = 10
{tex} \Rightarrow {/tex} x₁ + x₂ + x₃ = 5 ...... (vii)
Adding (ii),(iv)and (vi)
2(y₁ + y₂ + y₃) = 18
y₁ + y₂ + y₃ = 9 ....... (viii)
Subtracting (i), (iii) and (v) from (vii)
We get, x₁ = -1, x₂ = -5, x₃ = 11
Subtracting (ii), (iv) and (vi) from eq. (viii)
We get, y₁ = 7, y₂ = -3, y₃ = 5