According to ques,:
The vertices of ∆ABC are A (1, 4), B (− 3, 2) and C (− 5, − 3).
Now let us find the slopes of ∆ABC.
![\[Slope\text{ }of\text{ }AB\text{ }=\text{ }\left[ \left( 2\text{ }\text{ }4 \right)\text{ }/\text{ }\left( -3-1 \right) \right]~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5afb5943eadbdc5f02208dd7696fa3df_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-649cd287d7e6c96736558bb936b96467_l3.png "Rendered by QuickLaTeX.com")
And,
![\[Slope\text{ }of\text{ }BC\text{ }=\text{ }\left[ \left( -3\text{ }\text{ }2 \right)\text{ }/\text{ }\left( -5+3 \right) \right]~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-441c62476e9e357225758c20850fdbb1_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }5/2\text{ }~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-48e0ef9bbdef54123d06a4d5c33b4e91_l3.png "Rendered by QuickLaTeX.com")
And again,
![\[Slope\text{ }of\text{ }CA\text{ }=\text{ }\left[ \left( 4\text{ }+\text{ }3 \right)\text{ }/\text{ }\left( 1\text{ }+\text{ }5 \right) \right]~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8a914443254f4e12bf9113f1d17f2267_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }7/6~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9ae3568683cbcaeaaee1e90d4991b270_l3.png "Rendered by QuickLaTeX.com")
Thus, we have:
![\[Slope\text{ }of\text{ }CF\text{ }=\text{ }-2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-26b4d529c2dfed2cd2383962e0890efd_l3.png "Rendered by QuickLaTeX.com")
![\[Slope\text{ }of\text{ }AD\text{ }=\text{ }-2/5~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cd1b338d05fcba01f9e686d6fb09c040_l3.png "Rendered by QuickLaTeX.com")
And,
![\[Slope\text{ }of\text{ }BE\text{ }=\text{ }-6/7~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9c22d83f1f977b2beeec92a5cd8e2ce7_l3.png "Rendered by QuickLaTeX.com")
Hence,
Equation of CF is:
![\[y\text{ }+\text{ }3\text{ }=\text{ }-2\left( x\text{ }+\text{ }5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-02ba83f943215d142d2064560f1216f9_l3.png "Rendered by QuickLaTeX.com")
![\[y\text{ }+\text{ }3\text{ }=\text{ }-2x\text{ }\text{ }10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7a428fff19bb9b7fafdf6d91253561ec_l3.png "Rendered by QuickLaTeX.com")
or,
![\[2x\text{ }+\text{ }y\text{ }+\text{ }13\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-06ec203c989c6ce12997f4c35cbe0aca_l3.png "Rendered by QuickLaTeX.com")
Equation of AD is:
![\[y\text{ }\text{ }4\text{ }=\text{ }\left( -2/5 \right)\text{ }\left( x\text{ }\text{ }1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a9db918ebfbc61bf70b60204982b8dff_l3.png "Rendered by QuickLaTeX.com")
![\[5y\text{ }\text{ }20\text{ }=\text{ }-2x\text{ }+\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-adc40351b2915823ff2198dbabf66fe5_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[2x\text{ }+\text{ }5y\text{ }\text{ }22\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51070c3ecba6165378fc72cade9fb9de_l3.png "Rendered by QuickLaTeX.com")
Equation of BE is:
![\[y\text{ }\text{ }2\text{ }=\text{ }\left( -6/7 \right)\text{ }\left( x\text{ }+\text{ }3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-71de3ff1549ba35b7c6cb0de6d0e2884_l3.png "Rendered by QuickLaTeX.com")
![\[7y\text{ }\text{ }14\text{ }=\text{ }-6x\text{ }\text{ }18\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eb1cdb84878d5a56431ce43ac03d7eb5_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[6x\text{ }+\text{ }7y\text{ }+\text{ }4\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5d5838a61af06fa174f86edee2281de6_l3.png "Rendered by QuickLaTeX.com")
∴ The required equations are:
![\[~2x\text{ }+\text{ }y\text{ }+\text{ }13\text{ }=\text{ }0,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-818e751c43be63ed97eb8cdef58bcd8e_l3.png "Rendered by QuickLaTeX.com")
![\[2x\text{ }+\text{ }5y\text{ }\text{ }22\text{ }=\text{ }0,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dc00fba3290aeb47cbce2ebd448b716f_l3.png "Rendered by QuickLaTeX.com")
And
![\[6x\text{ }+\text{ }7y\text{ }+\text{ }4\text{ }=\text{ }0.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-15446809fd13ecef380e780afcd51990_l3.png "Rendered by QuickLaTeX.com")