Use the image to answer the question.

Question

A coordinate plane's axes range from 0 to 8, both by 1-unit increments. A triangle made up of vertices upper A, upper B, and upper C is plotted. The coordinates of the vertices are given.

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?

(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)
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
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Answer 1

To determine the ordered pairs of the three median bisectors, you need to find the midpoints of each side of the triangle formed by vertices A, B, and C. The medians of a triangle connect each vertex to the midpoint of the opposite side.

1. Find midpoints:

   • If the coordinates of vertices A, B, and C are provided, calculate the midpoints of each side:
     • Midpoint M1 between B and C.
     • Midpoint M2 between A and C.
     • Midpoint M3 between A and B.

2. Calculate the medians:

   • From vertex A to midpoint M1.
   • From vertex B to midpoint M2.
   • From vertex C to midpoint M3.

3. Determine the intersection point (centroid) of the medians, which is also the point where they meet.

Since I can't observe the image, I am unable to calculate the midpoints or medians without specific coordinates of vertices A, B, and C.

However, based on the response options provided, you can analyze which set of points might represent the centroids based on the coordinates likely corresponding to an actual triangle.

Please check your calculation of midpoints for every option listed and confirm which response matches.

If I had the original coordinates of the triangle, I'd be able to provide a concrete answer.