Question

The mid-point of the sides of a triangle are $(3,4),(4,1)$ and $(2,0)$. Find the coordinates of the vertices of the triangle.

Answer 1

Let the Verticex be $(x_a,y_a),(x_b,y_b),(x_c,y_c)$

According to question

$x_a+x_b=6\cdots \left(1\right)$

$x_b+x_c=8\cdots \left(2\right)$

$x_c+x_a=4\cdots \left(3\right)$

$x_a+x_b+x_c=18\cdots \left(4\right)$

$⟹x_a=1,x_b=5,x_c=3$

$y_a+y_b=8\cdots \left(1\right)$

$y_b+y_c=2\cdots \left(2\right)$

$y_c+y_a=0\cdots \left(3\right)$

$y_a+y_b+y_c=10\cdots \left(4\right)$

$⟹y_a=3,y_b=5,y_c=-3$