Question

a line segment has an endpoint at (-3, 9), and its midpoint is at (3,3). what is the ordered pair for the other endpoint of the line segment?

Answer 1

Start at (-3,9).  The increase in x from this point to the midpoint (3,3) is 6.  Add 6 to the x-coordinate of (3,3), obtaining 9, which is the x-coordinate of the other endpoint of the line segment.

Next, notice that y decreases by 6 from 9 to 3 as we travel from (-3,9) to (3,3).   Decrease y again by 6:  3 less 6 is -3.  So the y-coordinate of the other endpoint is -3.  

Thus, the coordinates of the other endpoint are (9, -3).

Let's check whether this is correct or not.  According to the midpoint formula, e find the x-coordinate of the midpoint by summing up the endpoint x values and dividing this sum by 2:  (-3+9)/2 = 3.  This agrees with the given midpoint (3,3).