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=(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=(8-(-2))/(3-7)=(10)/(-4)=-(5)/(2)`

Substitute to the equation (*):

`-(5)/(2)m_2=-1\ \ \ |\cdot\left(-(2)/(5)\right)\\\\m_2=(2)/(5)`

Answer: D. 2/5