AD is perpendicular to BC, therefore from the slope m₁ of BC and the slope m₂ of AD we have equation:
[tex]m_1m_2=-1[/tex] (*)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex]B(7,\ -2)\to x_1=7,\ y_1=-2\\C(3,\ 8)\to x_2=3,\ y_2=8[/tex]
Substitute:
[tex]m_1=\dfrac{8-(-2)}{3-7}=\dfrac{10}{-4}=-\dfrac{5}{2}[/tex]
Substitute to the equation (*):
[tex]-\dfrac{5}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{5}\right)\\\\m_2=\dfrac{2}{5}[/tex]
Answer: D. 2/5
