Question

21. Length of the median through C of triangle ABC with A(4,9) B(2,3) and
C(6,5) is​

Answer 1

Answer:

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Answer 2

Answer:

Length of the median AD is √10 units.

Step-by-step explanation:

Given :-

A(4,9), B(2,3) and  C(6,5) are the vertices of the ΔABC.

To find :-

Length of the median through C of ΔABC.

Solution :-

Draw CD (median) in ΔABC through C, then D will be the mid point of AB.

Applying midpoint formula :-

$\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}$

$\frac{4+2}{2}, \frac{9+3}{2}$

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

Now, we got the co-ordinates of D, applying distance formula :-

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{(6-3)^2+(5-6)^2}$

$\sqrt{(9)+(1)}$

$\sqrt{10}$

∴ Length of the median AD is √10 units.