Question

The midpoints 'D' , 'E' , 'F' of the sides of a ∆ ABC are (3, 4) , (8, 9) , (6, 7). Find the co-ordinate of the vertices of the triangle.

Answer 1

Heya Mate

(•) Given the Mid-points of a triangle, you can very easily do the following and get your Vertices ->

✓✓ Assume your desired vertices are :

$A( x_1 ,y_1),B( x_2 ,y_2),C( x_3 ,y_3)$

✓✓ Using mid-point formula :

$(i) \: \frac{x_1 +x_2 }{2} = 3$

$(ii) \: \frac{x_2 +x_3 }{2} = 8$

$(iii) \: \frac{x_3 +x_1 }{2} = 6$

$(iv) \: \frac{y_1 +y_2 }{2} = 4$

$(v) \: \frac{y_2 +y_3 }{2} = 9$

$(vi) \: \frac{y_3+y_1 }{2} = 7$

Now, Six Variables, Six Equations, Solve them to get ->

$A( x_1 ,y_1) \equiv ( 1,2) \\ \\ B( x_2 ,y_2)\equiv ( 5,6)\\ \\ C( x_3 ,y_3)\equiv ( 11,12)$

There you have your vertices ^_^

( Well umm, for the Equation solving part :p I'd suggest -> First add all equations with variable 'x' and then subtract individual equations and then do the same with 'y' )