In which quadrant does the ordered pair (5, -6) lie?

The coordinate (5,-6) lies in the fourth coordinate, because the first is x positive y positive, the second is x negative and y positive, the third is x negative and y negative, and the fourth is x positive y negative. This is x positive y negative, so it is in the fourth quadrant.

The bottom right hand quadrant (quadrant #4 in Algebraic terms)

The distance from point a to point c across the coordinate plane is aproxamatly 8.94 rounded to the nearest hundredth. you use a^2 + b^2 =c^2