They represent two points.
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If you are talking about the things in the perentheses, (5,-9), they are called ordered pairs. Ordered pairs help you find a location on a coordinate graph.
A coordinate graph is a graph of pairs of numbers that represent real-life situations.
Each ordered pair is made up of two numbers. A linear graph has an infinite number of pairs. An easy way to see this is look at the line y=x. This is a linear graph and any two of the same numbers will work! So there are an infinite number of ordered pairs.
Infinitely many. Each and every point on the graph gives rise to an ordered pair.
I'm not sure what you are asking. Sums represent either an increase of one quantity by another quantity, or a combination of two quantities. Two of anything is a pair. Did you mean to ask, "What are sums of pairs?" One common use of a pair in mathematics is an ordered pair, such as (2,3). This can represent a coordinate in a graph, or it can represent a vector. If pairs represent a vector, you add the components, so (2,3) + (40,50) = (42, 53).