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 (4,5), upper B (1,2), and upper C (6,2) 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
Skip to navigation

Answer 1

To find the coordinates of the medians' midpoints of the triangle with vertices A(4,5), B(1,2), and C(6,2), we need to identify the midpoints of each side of the triangle.

1. Midpoint of BC (creates median from A):

   • B(1,2) and C(6,2): \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + 6}{2}, \frac{2 + 2}{2} \right) = \left( \frac{7}{2}, 2 \right) = (3.5, 2) \]

2. Midpoint of AC (creates median from B):

   • A(4,5) and C(6,2): \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{4 + 6}{2}, \frac{5 + 2}{2} \right) = \left( \frac{10}{2}, \frac{7}{2} \right) = (5, 3.5) \]

3. Midpoint of AB (creates median from C):

   • A(4,5) and B(1,2): \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{4 + 1}{2}, \frac{5 + 2}{2} \right) = \left( \frac{5}{2}, \frac{7}{2} \right) = \left( 2.5, 3.5 \right) \]

Thus, the ordered pairs of the three median bisectors are:

• From B to C: (3.5, 2)
• From A to C: (5, 3.5)
• From A to B: (2.5, 3.5)

Now we can match these points with the options given:

The correct response is:

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