Given:
The vertices of the triangle are
![\[A\text{ }\left( 5,\text{ }4,\text{ }6 \right),\text{ }B\text{ }\left( 1,\text{ }-1,\text{ }3 \right)\text{ }and\text{ }C\text{ }\left( 4,\text{ }3,\text{ }2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c98b473f3d1f3a34d51695f4eac14ba3_l3.png "Rendered by QuickLaTeX.com")
By using the formulas let us find the coordinates of
![\[D\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9c4676f20ccd7810d5037433153eb5fe_l3.png "Rendered by QuickLaTeX.com")
and the length of
![\[AD\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2bac86ab21c8e8c6d1d22911b04c88d8_l3.png "Rendered by QuickLaTeX.com")
The distance between any two points
![\[\left( a,\text{ }b,\text{ }c \right)\text{ }and\text{ }\left( m,\text{ }n,\text{ }o \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-35c34c22a15e72bb736c916fe956b30a_l3.png "Rendered by QuickLaTeX.com")
is given by,
The section formula is given as
![\[AB\text{ }:\text{ }AC\text{ }=\text{ }5:3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d78d3fe6cddda0b52022f08575fda6c1_l3.png "Rendered by QuickLaTeX.com")
![\[BD:\text{ }DC\text{ }=\text{ }5:3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-35e8473de0647833e75f9ca0c81f9f81_l3.png "Rendered by QuickLaTeX.com")
So,
![\[m\text{ }=\text{ }5\text{ }and\text{ }n\text{ }=\text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-de993ef841c3e8afc111ded3ac714b6d_l3.png "Rendered by QuickLaTeX.com")
![\[B\left( 1,\text{ }-1,\text{ }3 \right)\text{ }and\text{ }C\left( 4,\text{ }3,\text{ }2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8f2f871208236dba00faa613e52200db_l3.png "Rendered by QuickLaTeX.com")
Coordinates of
using section formula:
