Question

The midpoints of the sides of a triangle are A(2,-1), B(1,3), and C(-3,1). Determine the vertices of the triangle.

Answer 1

Le (a,b), (c,d) and (e,f) be the vertices, then
\[
a+e=2\\ b+f=6\\
c+e=4\\ d+f=-2\\
a+c=-6\\ b+d=4
\]
Solve them and you find
\[\{a=-4,c=-2,b=6,d=-2,e=6,f=0\}
\]

Answer 2

How did you determine the equations?
a+e=2
b+f=6
c+e=4
d+f=−2
a+c=−6
b+d=4

Answer 3

Can you explain it please?

Answer 4

B=(1,3) is the midpoint of (a,b) and (e,f)
then a + e = 2(1) and b+f = 2(3)
Same for the others

Answer 5

oh, I see. I think I understand now. Thank You.

Answer 6

I got some different numbers for f, b, and d.
f=6-b

6-b+d=-2
d= -2-6+b
d=-8+b

-8+b+b=2
-8+2b=2
2b=10
b=5
_________________________
d+5=2
d=-3
___________________________-
f=6-5
f=1

Answer 7

I am not sure which parts are incorrect