Question

Side upper B upper C is labeled lowercase a. Side upper C upper A is labeled lowercase b. Side upper A upper B is labeled lowercase c. The coordinates of the vertices of the triangle are located as follows: upper A at left parenthesis 4 comma 5 right parenthesis, upper B at left parenthesis 1 comma 2 right parenthesis, and upper C at left parenthesis 6 comma 2 right parenthesis.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)
𝑐
=
(
1
,
2
)
, b=(4,5)
𝑏
=
(
4
,
5
)
, and a=(6,2)
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=(3,4)
𝑐
=
(
3
,
4
)
, b=(4.5,4)
𝑏
=
(
4.5
,
4
)
, and a=(4,2)
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=(1.5,1.5)
𝑐
=
(
1.5
,
1.5
)
, b=(1,1.5)
𝑏
=
(
1
,
1.5
)
, and a=(2.5,0)
𝑎
=
(
2.5
,
0
)

c equals left parenthesis 1.5 comma 1.5 right parenthesis , b equals left parenthesis 1 comma 1.5 right pare

Answer 1

Midpoints of the sides (the median bisectors) are:

- a (midpoint of BC) = ((1+6)/2, (2+2)/2) = (3.5, 2)
- b (midpoint of CA) = ((6+4)/2, (2+5)/2) = (5, 3.5)
- c (midpoint of AB) = ((4+1)/2, (5+2)/2) = (2.5, 3.5)

The medians are the segments A(4,5)→(3.5,2), B(1,2)→(5,3.5), and C(6,2)→(2.5,3.5). They meet at the centroid (4+1+6)/3, (5+2+2)/3 = (11/3, 3).