Yes, here's the provided text in MathJax notation:

Yes, you are correct. If \(P(2, m)\) is the midpoint of the line joining \(Q(m, n)\) and \(R(n, -4)\), we can use the midpoint formula to find the values of \(m\) and \(n\). The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) are given by \(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\).

Let \(Q(m, n)\) be \((x_1, y_1)\) and \(R(n, -4)\) be \((x_2, y_2)\). Then, the coordinates of the midpoint \(P\) are given by:

\(\left(\frac{{m + n}}{2}, \frac{{n - 4}}{2}\right)\)

Since \(P\) is also given as \((2, m)\), we can equate the coordinates to get a system of two equations:

\(\frac{{m + n}}{2} = 2\)

\(\frac{{n - 4}}{2} = m\)

To solve the simultaneous equations:

\(\frac{{m + n}}{2} = 2\)

\(\frac{{n - 4}}{2} = m\)

We can start by isolating one variable in one of the equations and substitute it into the other equation. Let's solve for \(n\) in terms of \(m\) from the second equation:

\(\frac{{n - 4}}{2} = m\)

Multiply both sides of the equation by 2:

n - 4 = 2m

Add 4 to both sides of the equation:

n = 2m + 4

Now we substitute this expression for \(n\) into the first equation:

\(\frac{{m + n}}{2} = 2\)

\(\frac{{m + (2m + 4)}}{2} = 2\)

Simplify the equation:

\(\frac{{3m + 4}}{2} = 2\)

Multiply both sides of the equation by 2:

3m + 4 = 4

Subtract 4 from both sides of the equation:

3m = 0

Divide both sides of the equation by 3:

m = 0

Now we substitute the value of m back into the equation we found for n:

n = 2m + 4

n = 2(0) + 4

n = 4

Therefore,m = 0 and n = 4.