Question

Calculate the area of triangle ABC with altitude CD, given A (-7, -1), B (-1, 5), C (0, 0), and D (-3, 3)

A. 21 square units
B. 9 square units
C. 18 square units
D. 18.5 square units

Answer 1

It is C. You don't C and D points. Just take determinant of points A and B and take absolute value of determinant and divide it by 2. (I hope you know a little bit about matrices and determinants) Let me:
\[\det(\left[\begin{matrix}-7 & -1 \\ -1 & 5\end{matrix}\right]) = -7 \times 5 - [(-1) \times (-1)] = -36\]
After this, we take absolute value of determinant and divide it by 2:
\[\frac{ \left| -36 \right| }{ 2 } = 18\]