Question

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=(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)
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
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Answer 1

The vertices are (1,2), (4,5), (6,2). The midpoints of the sides (the medians' bisectors) are

- midpoint of (1,2) and (4,5): ((1+4)/2,(2+5)/2) = (2.5,3.5)
- midpoint of (4,5) and (6,2): ((4+6)/2,(5+2)/2) = (5,3.5)
- midpoint of (6,2) and (1,2): ((6+1)/2,(2+2)/2) = (3.5,2)

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