The line $\mathrm{y}=\mathrm{mx}+\mathrm{n}$ is the reflection of $5\mathrm{x}-3\mathrm{y}=10$ about the line $\mathrm{y}=\mathrm{x}$, then find the value of n.

Let P be (a, a). It lies on 5x – 3y = 10
2a = 10
a = 5
Hence P (5, 5)

Now image of A (2, 0) in y = x is B (0, 2)
Hence the reflected line also passes through (0, 2).
Its equation is
$\mathrm{y}-2\frac{5-2}{5-0}(\mathrm{x}-0)\Rightarrow 5\mathrm{y}-10=3\mathrm{x}\Rightarrow \mathrm{y}=\frac{3\mathrm{x}}{5}+2$
Hence n = 2.