Use the image to answer the 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=(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)
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)

1 answer

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

To do this, we should identify each vertex's coordinates. However, since I don't have access to the image you referred to, I can't compute the midpoints directly.

However, the process would involve:

  1. Finding the midpoints of the line segments formed by pairs of vertices (sides of the triangle).
  2. The midpoints can be found using the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the endpoints.

Once you compute the midpoints, you can then determine coordinates corresponding to each median by taking the midpoint of the opposite side respective to each vertex.

You provided four options. To determine the correct answer using our findings:

  • Check each option based on calculated midpoints.
  • Confirm each response's pair of points matches the midpoints you calculate.

If you have the coordinates of A, B, and C, I can assist you in calculating the midpoints directly. Otherwise, please cross-check the midpoints with the options provided to choose the correct one.