Given:
The vertices of triangle ABC are:
![\[A\text{ }\left( -1,\text{ }-2 \right),\text{ }B\left( 0,\text{ }1 \right)\text{ }and\text{ }C\left( 2,\text{ }0 \right).\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-485f9ea3be16f85a2c345088749ee53e_l3.png "Rendered by QuickLaTeX.com")
Let us find the equation of median through A.
Hence, equation of BC is
On using the formula,
![\[x\text{ }+\text{ }2y\text{ }\text{ }2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-57bf067b753939449fd8a210d6ee3c9d_l3.png "Rendered by QuickLaTeX.com")
Let D be the midpoint of median AD,
![\[4y\text{ }+\text{ }8\text{ }=\text{ }5x\text{ }+\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c0a094b1c3410c59848174687ef8af0c_l3.png "Rendered by QuickLaTeX.com")
![\[5x\text{ }\text{ }4y\text{ }\text{ }3\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4b2f0b91db86bf659651635bbe3e393b_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line BC is:
![\[x\text{ }+\text{ }2y\text{ }\text{ }-2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-469c0d536884fbf8b032021b8193c1f6_l3.png "Rendered by QuickLaTeX.com")
The equation of median is:
![\[~5x\text{ }\text{ }-4y\text{ }\text{ }-3\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-916add11b410bf59858fdee4d62cb8d2_l3.png "Rendered by QuickLaTeX.com")