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EF has one endpoint E at (3,4). It's midpoint M is at (-4,6). what are the coordinates of the other endpoint F?

User Ikke
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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).

User Monte Hurd
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