Question

Can you explain d and e please.

Answer 1

Step-by-step explanation:

$d) \: \: \: \: \: \: \: \: \: mc = \sqrt{ {(8 - 0)}^{2} + {(0 + 2)}^{2} } = \sqrt{64 + 4} = \sqrt{68} \\ = 2 \sqrt{17} \: \: units. \\ \\ ac = \sqrt{ {(8 - 0)}^{2} + {(0 + 2)}^{2} } \\ = 2 \sqrt{17} \: \: \: \: units. \\ \\ \\ \\ e) \: \: \: \: \: \: \: \: \: \: m1(slope \: of \: am) = \frac{3 - 0}{4 - 8} = - \frac{3}{4} \\ \\ m2 = \frac{3 + 2}{0 + 2} = \frac{5}{2} \\ \\ \\ \tan( \alpha ) = | \frac{m1 - m2}{1 + m1m2} | = \frac{ \frac{5}{2} + \frac{3}{4} }{1 - \frac{5 \times 3}{2 \times 4} } = \frac{10 + 3}{8 - 15} = \frac{13}{ - 13} = - 1 \\ \\ \\ \\ \alpha = 135 \: degrees. \\ \\ required \: angle = angle(cma) = 135 \: degree. \\ \\ \\ \\ \\ area \: of \: triangle \: cma = 16 \: \: {units}^{2} .(explained \: in \: diagram \: attached)$