Question

50 POINTS AND MARK BRAINLIEST

Answer 1

Step-by-step explanation:

a) Using the distance formula,

$RS=\sqrt{(2-4)^{2}+(3-4)^{2}}=\sqrt{4+1}=\boxed{\sqrt{5}}\\ST=\sqrt{(4-5)^{2}+(4-0)^{2}}=\sqrt{1+16}=\boxed{\sqrt{17}}\\RT=\sqrt{(2-5)^{2}+(3-0)^{2}}=\sqrt{9+9}=\boxed{3\sqrt{2}}$

b) Using the slope formula,

$m_{\overline{RS}}=\frac{4-3}{4-2}=\boxed{\frac{1}{2}}\\m_{\overline{ST}}=\frac{0-4}{5-4}=\boxed{-4}\\m_{\overline{RT}}=\frac{0-3}{5-2}=\boxed{-1}$

c) The triangle is scalene because each of the sides is of a different length.