Question

Fund the area of triangle ABC, whose
coordinates are fA. AC6, -6), B (3,-2) ,c[5, 2]
then find the length of the median AD​

Answer 1

Answer:

$Area \: \Delta = \frac{1}{2} | \binom{6}{- 6} \binom{3}{ - 2} \binom{5}{2} \binom{6}{ - 6} | \\ = \frac{1}{2} |(6 \times - 2 + 3 \times 2 + 5 \times - 6 + 3 \times 6 + 5 \times 2 - 6 \times 2)| \\ = \frac{1}{2} \times | - 20| \\ = \frac{1}{2} \times 20 = 10 \: \: {unit}^{2}$

length of Base , BC =

$\sqrt{( {3 - 5)}^{2} + ( { - 2 - 2)}^{2} } \\ = \sqrt{ {( - 2)}^{2} + {( - 4)}^{2} } \\ = \sqrt{4 + 16} \\ = \sqrt{20} \\ = 2 \sqrt{5} \: \:u nit$