Question

Length of the median through C of triangle ABC with A(4,9) B(2,3) and

C(6,5) is answer in units​

Answer 1

Answer:

√10 units

Step-by-step explanation:

median from a vertex meets the opposite side at midpoint

midpoint of AB,D=(3,6)

now length of median = distance between D and C =√3^2+1^2=√10 units

Answer 2

Answer:

Length of the median through C of triangle ABC is $\sqrt{10}$ units​

Step-by-step explanation:

Given the coordinates  A(4,9) B(2,3) and C(6,5) of triangle ABC.

Let CD be the median through C of triangle ABC.

Then D is the midpoint of AB.

Using the midpoint point formula,

                 $\Big(\frac{x_{1} +x_{2}}{2} , \frac{y_{1} +y_{2}}{2}\Big)=\Big(\frac{4 +2}{2} , \frac{9+3}{2}\Big)$

                                         $=\Big(\frac{6}{2} , \frac{12}{2}\Big)=(3 ,6)$

Length of the median CD is

               $\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}}=\sqrt{(6-3 )^{2} +(5-6 )^{2}}$

                                                       $=\sqrt{(3 )^{2} +(-1 )^{2}}=\sqrt{9 +1}$

                                                       $=\sqrt{10}units$

Therefore the length of the median through C is $\sqrt{10}$ units​