Question

How do you label the points to use in the distance and midpoint formula?

(x1,y2) and (x2,y1)
(x1,y1) and (x2,y2)
(x1,x2) and (y1,y2)
(x2,x1) and (y2,y1)

Answer 1

Answer: Choice B

(x1,y1) and (x2,y2)

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Reason:

Each point is of the form (x,y) where x is first. Think of the ordering of the letters in the alphabet.

Then we stick 1's or 2's to each point to help distinguish the points from one another.

Writing (x1,y1) is the same as saying
`(\text{x}_1, \text{y}_1)`, and similarly (x2,y2) is the same as
`(\text{x}_2, \text{y}_2)`. We cannot mix up the 1's and 2's. They must remain separate.

This notation is helpful for the distance formula, midpoint formula, and also the slope formula. There are likely other useful applications as well.