Question

Geometry math question no Guessing and Please show work thank you

Answer 1

AD is perpendicular to BC, therefore from the slope m₁ of BC and the slope m₂ of AD we have equation:

$m_1m_2=-1$ (*)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have

$B(7,\ -2)\to x_1=7,\ y_1=-2\\C(3,\ 8)\to x_2=3,\ y_2=8$

Substitute:

$m_1=\dfrac{8-(-2)}{3-7}=\dfrac{10}{-4}=-\dfrac{5}{2}$

Substitute to the equation (*):

$-\dfrac{5}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{5}\right)\\\\m_2=\dfrac{2}{5}$

Answer: D. 2/5