To prove that all three medians of a triangle meet at the same point, the medians of each side A(4,5) B(1,2) C(6,2)must be found. What are the ordered pairs of the three median bisectors? (1 point) Responses c=(3,4) , b=(4.5,4) , and a=(4,2) c equals left parenthesis 3 comma 4 right parenthesis , b equals left parenthesis 4.5 comma 4 right parenthesis , and a equals left parenthesis 4 comma 2 right parenthesis c=(1,2) , b=(4,5) , and a=(6,2) c equals left parenthesis 1 comma 2 right parenthesis , b equals left parenthesis 4 comma 5 right parenthesis , and a equals left parenthesis 6 comma 2 right parenthesis c=(2.5,3.5) , b=(5,3.5) , and a=(3.5,2) c equals left parenthesis 2.5 comma 3.5 right parenthesis , b equals left parenthesis 5 comma 3.5 right parenthesis , and a equals left parenthesis 3.5 comma 2 right parenthesis c=(1.5,1.5) , b=(1,1.5) , and a=(2.5,0)
To find the medians of a triangle, we need to find the midpoints of each side of the triangle.
The midpoint formula is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
For side AB:
Midpoint = ((1 + 4)/2, (2 + 5)/2)
Midpoint = (5/2, 7/2)
Midpoint = (2.5, 3.5)
For side AC:
Midpoint = ((1 + 6)/2, (2 + 2)/2)
Midpoint = (7/2, 4/2)
Midpoint = (3.5, 2)
For side BC:
Midpoint = ((4 + 6)/2, (5 + 2)/2)
Midpoint = (10/2, 7/2)
Midpoint = (5, 3.5)
Therefore, the ordered pairs of the three median bisectors are:
a = (3.5, 2)
b = (2.5, 3.5)
c = (5, 3.5)
So, the correct answer is:
c = (3.5, 2) , b = (2.5, 3.5) , and a = (5, 3.5)