If the image of the point $(- 1, 2)$ in the line $4 x + 3 y - p = 0$ is the point $(3, 5)$ , then find the value of $p$ .

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Solution

$\begin{matrix} m i d - p o i n t o f (- 1, 2) a n d (3, 5) (\frac{3 - 1}{2}, \frac{5 + 2}{2}) = (1, \frac{7}{2}) 4 (1) + 3 \times \frac{7}{2} - p = 0 p = 4 + \frac{21}{2} = \frac{29}{2} \end{matrix}$

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