If AD is the altitude to BC, then AD is perpendicular to BC.
The formula of a slope:
[tex]A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]
If [tex]k:y=m_1x+b_1;\ l:y=m_2x+b_2[/tex] then [tex]k\ \perp\ l\iff m_1m_2=-1[/tex]
Calculate the slope of BC:
[tex]B(7;\ -2);\ C(3;\ 8)\\\\m_1=\dfrac{8-(-2)}{3-7}=\dfrac{10}{-4}=-\dfrac{5}{2}[/tex]
Calculate the slope of AD:
[tex]-\dfrac{5}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{5}\right)\\\\m_2=\dfrac{2}{5}[/tex]
Answer: D. 2/5
