Question

Geometry math question no Guessing and Please show work thank you

Answer 1

If AD is the altitude to BC, then AD is perpendicular to BC.

The formula of a slope:

`A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\m=(y_B-y_A)/(x_B-x_A)`

If
`k:y=m_1x+b_1;\ l:y=m_2x+b_2` then
`k\ \perp\ l\iff m_1m_2=-1`

Calculate the slope of BC:

`B(7;\ -2);\ C(3;\ 8)\\\\m_1=(8-(-2))/(3-7)=(10)/(-4)=-(5)/(2)`

Calculate the slope of AD:

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

Answer: D. 2/5