Final answer:
The other endpoint F of the line segment with one endpoint E at (3,4) and midpoint M at (-4,6) has coordinates (-11,8). This was determined by using the midpoint formula in reverse.
Step-by-step explanation:
To find the coordinates of the other endpoint F when you know one endpoint E and the midpoint M of a line segment EF, you can use the midpoint formula in reverse. The midpoint M of EF has coordinates (-4,6), and one endpoint E has coordinates (3,4).
Since M is the midpoint, its coordinates are the averages of the coordinates of E and F. If (xF, yF) are the coordinates we want to find for F, we can set up the following equations based on the midpoint formula:
(xE + xF)/2 = xM
(yE + yF)/2 = yM
Substituting the known values gives us:
(3 + xF)/2 = -4
(4 + yF)/2 = 6
Solving these equations yields:
xF = -4 * 2 - 3 = -11
yF = 6 * 2 - 4 = 8
Therefore, the coordinates of endpoint F are (-11,8).