Given:
![\[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\text{ }=\text{ }A\text{ }\left( 2,\text{ }1 \right),\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ba96c08c03c175490f2292c55d785ff9_l3.png "Rendered by QuickLaTeX.com")
![\[\theta ~=~\pi /4\text{ }=\text{ }45{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d9c21ec1b2c8a06c6594e1fd015a1c67_l3.png "Rendered by QuickLaTeX.com")
Let us find the length AB.
By using the formula,
The equation of the line is given by:
![\[x\text{ }\text{ }y\text{ }\text{ }1\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-68c01ac4628390872be7800e5bee19a7_l3.png "Rendered by QuickLaTeX.com")
Let ,
![\[AB\text{ }=\text{ }r\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-be6fe664ebc1165ed560b2d968f88a42_l3.png "Rendered by QuickLaTeX.com")
Then, the coordinate of B is given by:
A straight line drawn through the point A (2, 1) making an angle π/4 with positive x–axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.
A straight line drawn through the point A (2, 1) making an angle π/4 with positive x–axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.