Question

When you use the midpoint formula can you take either points as x ,y? Why or why not ?

Answer 1

Answer:

Yes, we can take either points as x and y because addition is commutative

Step-by-step explanation:

First of all, the midpoint formula is given as;

(x, y) = [((x₁ + x₂)/2), ((y₁ + y₂)/2)]

For example, if we assume that we have two endpoints having coordinates as (2, 5) and (4, 7)

Now, let (2, 5) represent the first coordinate and (4, 7) represent the second coordinate.

Thus, Coordinates of midpoint = [((2 + 4)/2), ((5 + 7)/2)]

This gives;

(x, y) = (3, 6)

Now,if we change the order of the coordinates by making (4, 7) to be the first coordinate and (2, 5) to be the second coordinate. Thus;

Coordinates of midpoint = [((4 + 2)/2), ((7 + 5)/2)] = (3, 6)

We can see that the coordinates of the midpoint remains the same even after interchanging the coordinates as first and second.

This is because we are adding two numbers and addition is commutative (in commutative properties, changing the order of the operands will not change the result). Thus, it doesn't matter in which order we have the endpoints.