![\[\left( i \right)\text{ }\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8d5338de38ce9340e4fd40be496a54b1_l3.png "Rendered by QuickLaTeX.com")
Given:
![\[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\text{ }=\text{ }\left( 0,\text{ }0 \right),~\left( {{x}_{2}},\text{ }{{y}_{2}} \right)\text{ }=\text{ }\left( 2,\text{ }-2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79326b33244d1ca342912f8d34bd2623_l3.png "Rendered by QuickLaTeX.com")
The equation of the line passing through the two points :
![\[\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9ebb557387495905e4247d71f1a11252_l3.png "Rendered by QuickLaTeX.com")
is
According to formula,
![\[y\text{ }=\text{ }\text{ }x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-749ac05229af182c17e9d622b25ad9a0_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line is
![\[y\text{ }=\text{ }-x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3b4f8e93eba16a042b41495dc55cc5c6_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{ii} \right)~\left( a,\text{ }b \right)\text{ }and\text{ }\left( a\text{ }+\text{ }c\text{ }sin\text{ }\alpha ,\text{ }b\text{ }+\text{ }c\text{ }cos\text{ }\alpha \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e6bfab660139b78747f66d327842421_l3.png "Rendered by QuickLaTeX.com")
Given:
![\[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b2aaa5964aa95122649b7d8b96c0f036_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( a,\text{ }b \right),\text{ }\left( {{x}_{2}},\text{ }{{y}_{2}} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3917097018a83ac9d0122317fc36a2a4_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( a\text{ }+\text{ }c\text{ }sin\text{ }\alpha ,\text{ }b\text{ }+\text{ }c\text{ }cos\text{ }\alpha \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7c507f6b45da5af79ca750bdd71185a1_l3.png "Rendered by QuickLaTeX.com")
hence, the equation of the line passing through the two points:
![\[~\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a711416826ab20f2583d0ba7b2a0b4fe_l3.png "Rendered by QuickLaTeX.com")
is,
By using the formula,
![\[y\text{ }\text{ }b\text{ }=\text{ }cot\text{ }\alpha \text{ }\left( x\text{ }\text{ }a \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-363b0614b000f6333ab9a52024731b7e_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line is:
![\[~y\text{ }\text{ }b\text{ }=\text{ }cot\text{ }\alpha \text{ }\left( x\text{ }\text{ }a \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f64a9976c252f6bfd067439285575f44_l3.png "Rendered by QuickLaTeX.com")