4. Supplementary angles together make a straight line (two right angles). So BOE is supplementary to BOC
Answer: ∠BOE
5. Distance and midpoint between (4,-2), (6,8)
![d = √( (6-4)^2 + (8 - -2)^2) = √(2^2+10^2)=√(104)=2 √(26)](https://img.qammunity.org/2019/formulas/mathematics/college/7zlztlqpna7aemovebg7lsbkia8nblmjbx.png)
midpoint
![\left((4 + 6)/(2), (-2 + 8)/(2) \right) = (5, 3)](https://img.qammunity.org/2019/formulas/mathematics/college/95g1d4plcmnb0w897shbqng79pjp8mjx5h.png)
Answer: distance 2√26, midpoint (5, 3)
6.That's a rectangle oriented parallel to the axes, width parallel to the x axis of 7 - -3 = 10 and length along y of 1 - - 4 = 5, so an area of 10(5)=50
Answer: 50