Given:
![\[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\text{ }=\text{ }A\text{ }\left( 3,\text{ }4 \right),\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ee2d56701759dea224892f1c4a926d60_l3.png "Rendered by QuickLaTeX.com")
![\[~\theta ~=\text{ }\pi /6\text{ }=\text{ }30{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-912b71d26448949047ce3c199ccf3b80_l3.png "Rendered by QuickLaTeX.com")
To find the length PQ.
By using the formula,
The equation of the line is given by:
![\[~x\text{ }\text{ }\surd 3\text{ }y\text{ }+\text{ }4\surd 3\text{ }\text{ }3\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6fdbb9211b7b57e0095985f9fa471622_l3.png "Rendered by QuickLaTeX.com")
Let
![\[PQ\text{ }=\text{ }r\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ede4dcc9930783b927cade544f77f20a_l3.png "Rendered by QuickLaTeX.com")
Then, the coordinate of Q are given by:
If the straight line through the point P(3, 4) makes an angle π/6 with the x–axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.
If the straight line through the point P(3, 4) makes an angle π/6 with the x–axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.