Question

In triangle ABC the midpoints of sides BC,CA and AB are (1,0),(3,5) and (-2,4) respectively .Find the coordinates of threee vertices A,B and C.

Answer 1

A(a,b),B(c,d),C(e,f)

(A+B)/2=(2,1)(a+c)/2=(b+d)/2=1

a+c=4 b+d=2

(B+C)/2=(1,0) c+e=2 d+f=0

(C+A)/2=(21,3) a+e=42 b+f=6

Six equations in six unknowns, no problem.

Subtracting c+e=2 from a+c=4 gives

a−e=2

a+e=42

2a=44

a=22

e=a−2=20

c=4−a=−18

Subtracting d+f=0 from b+d=2 gives

b−f=2

b+f=6

2b=8

b=4

f=b−2=2

d=−f=−2

Putting it all together,  

A(22,4),B(−18,−2),C(20,2)

Answer 2

Answer:

A (0,9) , B (-4, -1) , C (6, 1)