Line $L_{1}$ passes through the point $(2,-1)$ and has slope $m$. Line $L_{2}$ passes through $(m,3)$ and is perpendicular to $L_{1}$. If the two lines intersect at a point whose $x$-coordinate is 1, find the possible values of $m$ and the coordinates of the intersection point.

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m = \frac{-5 \pm \sqrt{29}}{2}, intersection point (1, \frac{3 \mp \sqrt{29}}{2})

Neco 2021 Mathematics Question 35

Line \(L_{1}\) passes through the point \((2,-1)\) and has slope \(m\). Line \(L_{2}\) passes through \((m,3)\) and is perpendicular to \(L_{1}\). If the two lines intersect at a point whose \(x\)-coordinate is 1, find the possible values of \(m\) and the coordinates of the intersection point.

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