Question

10 Find the lengths of the medians AD and BE of triangle ABC whose vertices are A(7,-3), B(5,3) and C(3,-1). [CBSE 2014]

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Answer 1

The vertex of triangle ABC are A(7,-3), B (5,3), C (3,-1)

Condider a triangle ABC as shown in figure attached below

We have to find the length of median through vertex A which is length of AD

The point D(x, y) is the midpoint of BC

So, midpoint can be calculated as follows:-

$\bf \: x=\frac{x_{1}+x_{2}}{2} ; y=\frac{y_{1}+y_{2}}{2}$

Here for midpoint of BC, we have:

$\mathrm{B}\left(x_{1}, y_{1}\right)=(5,3) \text { and } C\left(x_{2}, y_{2}\right)=(3,-1)$

$\tt \: x=\frac{5+3}{2}=\frac{8}{2}=4 \\ \text { and } \\ \tt \: y=\frac{3-1}{2}=\frac{2}{2}=1$

The coordinates of D are (4,1)

The length of median AD = Distance Between A and D

$\begin{gathered}\begin{array}{l}{\mathrm{D}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_2 - y_1\right)^{2}}} \\\\ {\mathrm{D}=\sqrt{(4-7)^{2}+(1+3)^{2}}} \\\\ {\mathrm{D}=\sqrt{(-3)^{2}+(4)^{2}}} \\\\ {\mathrm{D}=\sqrt{9+16}=\sqrt{25}=5}\end{array}\end{gathered}$

Hence, the length of median is 5 units

Answer 2

Step-by-step explanation:

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