Question

A(5,1), B(1,5) and C(-3,-1) are the vertices of triangle ABC. Find the lenght of the median AD

Answer 1

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Answer 2

Answer:

The length of the median AD= $\sqrt{37}$

Step-by-step explanation:

Since D is the midpoint of BC , thus

Coordinates of D= $(\frac{1+(-3)}{2},\frac{5+(-1)}{2})$

Coordinates of D=$(-1,2)$

Now, The length of AD =$\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}$

=$\sqrt{(1-2)^{2}+(5-(-1))^{2}}$

=$\sqrt{(-1)^{2}+6^2}$

=$\sqrt{37}$

Thus, the length of the median AD= $\sqrt{37}$