Given:
The rectangle formed by the lines,
![\[x\text{ }=\text{ }a,\text{ }x\text{ }=\text{ }a,\text{ }y\text{ }=\text{ }b\text{ }and\text{ }y\text{ }=\text{ }b\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6bc509aa35676b777676baea62928b59_l3.png "Rendered by QuickLaTeX.com")
It is clear that, the vertices of the rectangle are:
![\[A\text{ }\left( a,\text{ }b \right),\text{ }B\text{ }\left( a,\text{ }b \right),\text{ }C\text{ }\left( a,\text{ }b \right)\text{ }and\text{ }D\text{ }\left( a,\text{ }b \right)\text{ }.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-424aa6751dcf2d9754fa5baf6821b1f0_l3.png "Rendered by QuickLaTeX.com")
The diagonal passing through A (a, b) and C (a’, b’) is
By using the formula,
![\[\left( a\text{ }\text{ }-a \right)y\text{ }\text{ }-b\left( a\text{ }\text{ }-a \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e89dc83fcdaa288cb1a4a336f80004d7_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( -b\text{ }\text{ }-b \right)x\text{ }\text{ }a\left( b\text{ }\text{ }b \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-67896cbe12bbe2f509a3f5bd6a38858a_l3.png "Rendered by QuickLaTeX.com")
and
![\[\left( a\text{ }\text{ }a \right)\text{ }\text{ }\left( b\text{ }\text{ }b \right)x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6552f7b3d4876157e022e11d0b14dcc7_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }ba\text{ }\text{ }ab\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2645122d45bb8e6628f0170afc6bbeed_l3.png "Rendered by QuickLaTeX.com")
In the same way, the diagonal passing through B (a’, b) and D (a, b’) is
By using the formula,
![\[\left( a\text{ }\text{ }a \right)y\text{ }\text{ }b\left( a\text{ }\text{ }a \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8a2c4dad4b406a76046f945df7b85445_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( b\text{ }\text{ }b \right)x\text{ }\text{ }a\text{ }\left( b\text{ }\text{ }b \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-753f7269e5b7c86f31614b45a3aaa3e9_l3.png "Rendered by QuickLaTeX.com")
And
![\[\left( a\text{ }\text{ }a \right)\text{ }+\text{ }\left( b\text{ }\text{ }b \right)x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bb457071b7acc4605e9939faa47198d8_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }ab\text{ }\text{ }ab\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ed96b7f872677956976e18f894f29648_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of diagonals are:
![\[~y\left( a\text{ }\text{ }a \right)\text{ }\text{ }x\left( b\text{ }\text{ }b \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4269606ebd1a11bedf30238d04fc238e_l3.png "Rendered by QuickLaTeX.com")
And
![\[y\left( a\text{ }\text{ }a \right)\text{ }+\text{ }x\left( b\text{ }\text{ }b \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eaf5acc440bcbd0f87fbffb8bc3f332c_l3.png "Rendered by QuickLaTeX.com")
