Given:

Vertices of ΔPQR for example \[\mathbf{P}\text{ }\left( \mathbf{2},\text{ }\mathbf{1} \right),\text{ }\mathbf{Q}\text{ }\left( -\text{ }\mathbf{2},\text{ }\mathbf{3} \right)\text{ }\mathbf{and}\text{ }\mathbf{R}\text{ }\left( \mathbf{4},\text{ }\mathbf{5} \right)\]

Leave RL alone the middle of vertex R.

Along these lines, L is a midpoint of PQ.

We realize that the midpoint equation is given by

\[\therefore \mathbf{L}\text{ }=\text{ }\left( \mathbf{0},\text{ }\mathbf{2} \right)\]

We realize that the condition of the line going through the focuses (x1, y1) and (x2, y2) is given by

\[\mathbf{y}\text{ }\text{ }\mathbf{5}\text{ }=\text{ }-\text{ }\mathbf{3}/\text{ }-\text{ }\mathbf{4}\text{ }\left( \mathbf{x}-\mathbf{4} \right)\]

\[\left( -\text{ }\mathbf{4} \right)\text{ }\left( \mathbf{y}\text{ }\text{ }\mathbf{5} \right)\text{ }=\text{ }\left( -\text{ }\mathbf{3} \right)\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{4} \right)\]

\[-\text{ }\mathbf{4y}\text{ }+\text{ }\mathbf{20}\text{ }=\text{ }-\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{12}\]

\[-\text{ }\mathbf{4y}\text{ }+\text{ }\mathbf{20}\text{ }+\text{ }\mathbf{3x}\text{ }\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{0}\]

\[\mathbf{3x}\text{ }\text{ }\mathbf{4y}\text{ }+\text{ }\mathbf{8}\text{ }=\text{ }\mathbf{0}\]

∴ The condition of middle through the vertex R is \[\mathbf{3x}\text{ }\text{ }\mathbf{4y}\text{ }+\text{ }\mathbf{8}\text{ }=\text{ }\mathbf{0}.\]