Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:
A (4,5)
B (-4,-5)
C (4,-5)

Hint: In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Complete step by step answer:
First of all let us try to demonstrate a coordinate system

The First quadrant is the top right quadrant in the system where both x and y coordinates remain Positive
The second quadrant is the top left quadrant in the system given where x is in negative and y is in positive.
The third quadrant is the left bottom one where both x and y coordinates are in negative
The last one is the fourth quadrant where the x points remain positive and the y becomes negative.
A. Point A is given as (4, 5) Clearly both the points are positive which means that the Point a belongs to the first quadrant.
B. Point B is given as (-4, -5) Clearly both the points x and y are in negative which clearly means that it belongs to the third quadrant.
C. Point C is given as (4, -5) Now here we can see that the x coordinate is in positive and the y-ordinate is in negative which clearly means that it belongs to the fourth quadrant.

Note: Coordinates systems are often used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, circles or spheres. It may occur that systems of coordinates for two different sets of geometric figures are equivalent in terms of their analysis.