Triangle midpoints

Determine coordinates of triangle ABC vertices if we know triangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.

Correct answer:

Ax =  3
Ay =  2
Bx =  -3
By =  4
Cx =  5
Cy =  8

Step-by-step explanation:


(a+c)/2=0
(b+d)/2=3
(c+f)/2=1
(d+g)/2=6
(a+f)/2=4
(b+g)/2=5

a+c = 0
b+d = 6
c+f = 2
d+g = 12
a+f = 8
b+g = 10

Row 5 - Row 1 → Row 5
a+c = 0
b+d = 6
c+f = 2
d+g = 12
-c+f = 8
b+g = 10

Row 6 - Row 2 → Row 6
a+c = 0
b+d = 6
c+f = 2
d+g = 12
-c+f = 8
-d+g = 4

Row 5 + Row 3 → Row 5
a+c = 0
b+d = 6
c+f = 2
d+g = 12
2f = 10
-d+g = 4

Row 6 + Row 4 → Row 6
a+c = 0
b+d = 6
c+f = 2
d+g = 12
2f = 10
2g = 16


g = 16/2 = 8
f = 10/2 = 5
d = 12-g = 12-8 = 4
c = 2-f = 2-5 = -3
b = 6-d = 6-4 = 2
a = 0-c = 0+3 = 3

a = 3
b = 2
c = -3
d = 4
f = 5
g = 8

Our linear equations calculator calculates it.



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