The midpoint of \overline{\text{AB}} AB is M(1, 3)M(1,3). If the coordinates of AA are (4, 1)(4,1), what are the coordinates of BB?

Answer 1

If the midpoint of AB is (1,3). and the coordinates of A are (4,1), the coordinates of B can be found by creating an equation using the midpoint formula M=((x₁+x₂)/2 , (y₁+y₂)/2)

B's x value can be found using the equation 1 = (4+x)/2 by setting the x value of the midpoint equal to the x value portion of the formula with A's value substituted.

1 = (4+x)/2

2 = 4+x

-2 = x

B's y value can be found using the same method, but using y values from the points. 3 = (1+y)/2

6 = 1+y

5 = y

B's coordinates are (-2,5)