In the \(xy\)-coordinate axis, a perpendicular line \(AD\) is drawn from the point \(A(2,4)\) on the line \(x + y = 10\)

In the \(xy\)-coordinate axis, a perpendicular line \(AD\) is drawn from the point \(A(2,4)\) on the line \(x + y = 10\) and it is extended till \(E,\) such that \(AD = DE.\) Find the coordinate of \(E?\)

A. \((-6,-8)\)

B. \(\left(\dfrac{55}{13}, \dfrac{44}{13}\right)\)

C. \((6, 8)\)

D. \((11, 5)\)

E. \((15,15)\)

Answer: C

Source: e-GMAT