Question

If the coordinates of the midpoints if a triangle are (10,5),(8,4),(6,6), then find the coordinates of its vertices ..

Answer 1

Answer:

Step-by-step explanation:

say vertices A(x1,y1),B(x2,y2),C(x3,y3)

But midpoints are given.

AB midpoint =(10,5)

BC midpoint =(8,4)

CA midpoint =(6,6)

i.e (x1+x2/2,y1+y2/2)=(10,5)

x1+x2=20

y1+y2=10

Similarly

x2+x3=16

y2+y3=8

And

x1+x3=12

y1+y3=12

By solving the 6 equations we can get x1,x2,y1,y2,x3,y3.

Finally A(x1,y1)=(8,7)

B(x2,y2)=(12,3)

C(x3,y3)=(4,5)