Question

Find the midpoint, M, of AB

A = (1,0) B = (5,2)

Answer 1

(2, 1)

Explanation:

Midpoint formula:

M =
`((x_(2) - x_(1))/(2), (y_(2)-y_(1))/(2))`

Where (x1, y1) represents the first set of coordinates and (x2, y2) represents the second set of coordinates. We are essentially averaging the x and y coordinates of the endpoints.

In this case, we are given:

Endpoint = (1, 0)

Another Endpoint = (5, 2)

Let's call (1, 0) the first pair and (5, 2) the second pair (it really doesn't matter which order you arrange them in, so like (5, 2) could be the first pair and (1, 0) the second).

Now plug them into our formula:

M =
`((x_(2) - x_(1))/(2), (y_(2)-y_(1))/(2))`

M =
`((5 - 1)/(2), (2-0)/(2))`

(subtraction before division)

M =
`((4)/(2), (2)/(2))`

(now divide/simplify)

M = (2, 1)

The midpoint of endpoints A (1, 0) and B (5, 2) is (2, 1).

Answer 2

M = (3,1)

Find the change in c and the change in y so the change in x is 4 units and the change in y is 2 units. Divide both chnages by two and add them to the factors of A.
4/2=2 and 2/2=1
(1,0) + (2,1) = (3,1)