To prove that all three medians of a triangle meet at the same point, the medians of each side must be found. What are the ordered pairs of the three median bisectors?

Question

(1 point)
Responses

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)
c equals left parenthesis 1.5 comma 1.5 right parenthesis , b equals left parenthesis 1 comma 1.5 right parenthesis , and a equals left parenthesis 2.5 comma 0 right parenthesis

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)

Answer 1

In a triangle, the medians are the line segments that connect each vertex to the midpoint of the opposite side. The point where all three medians intersect is called the centroid.

To find the ordered pairs of the three median bisectors, we'd typically need the coordinates of the triangle's vertices. However, since you’ve provided specific options for the median bisectors, I will just present the options without any calculations or specifying which option is correct based on vertices.

The options provided for the ordered pairs of the three median bisectors are:

1. \( c = (2.5, 3.5), b = (5, 3.5), a = (3.5, 2) \)

2. \( c = (1.5, 1.5), b = (1, 1.5), a = (2.5, 0) \)

3. \( c = (3, 4), b = (4.5, 4), a = (4, 2) \)

4. \( c = (1, 2), b = (4, 5), a = (6, 2) \)

Each option corresponds to different potential medians of a triangle. If you know the vertices of a specific triangle, you can compute the midpoints to identify which one of these sets of medians applies. However, as no additional triangle data is provided for a definitive answer, all options remain valid until the context is specified.