Question

unit 6 formal proofs > lesson 9 medians of a triangle back to intro page 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)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find mid - point of side $a$ (between $B(1,2)$ and $C(6,2)$)

Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(6,2)$. Then the mid - point $M_{a}$ is $(\frac{1 + 6}{2},\frac{2+2}{2})=(\frac{7}{2},2)$.

Step3: Find mid - point of side $b$ (between $A(4,5)$ and $C(6,2)$)

Let $(x_1,y_1)=(4,5)$ and $(x_2,y_2)=(6,2)$. Then the mid - point $M_{b}$ is $(\frac{4 + 6}{2},\frac{5 + 2}{2})=(5,\frac{7}{2})$.

Step4: Find mid - point of side $c$ (between $A(4,5)$ and $B(1,2)$)

Let $(x_1,y_1)=(4,5)$ and $(x_2,y_2)=(1,2)$. Then the mid - point $M_{c}$ is $(\frac{4+1}{2},\frac{5 + 2}{2})=(\frac{5}{2},\frac{7}{2})$.

Answer:

$(\frac{7}{2},2),(5,\frac{7}{2}),(\frac{5}{2},\frac{7}{2})$