Question

If the endpoints of EF are E(XE​,YE​) and A(XA​,YA​), what are the coordinates of the midpoint of EF?

A) (2XE​+XA​​,2YE​+YA​​)
B) (2XE​−XA​​,2YE​−YA​​)
C) (2XE​⋅XA​​,2YE​⋅YA​​)
D) (2XE​​,2YE​​)

Answer 1

The coordinates of the midpoint of line segment EF with endpoints E(XE, YE) and A(XA, YA) are obtained using the midpoint formula: M = (\((XE + XA)/2, (YE + YA)/2\)). Therefore, the correct answer is Option A.

Step-by-step explanation:

The question asks for the coordinates of the midpoint of line segment EF with endpoints E(XE, YE) and A(XA, YA). To find the midpoint of a line segment in a coordinate plane, we use the midpoint formula, which is the average of the x-coordinates and the y-coordinates of the endpoints.

The midpoint formula is given by:

M = \(\left(\frac{{XE + XA}}{2}, \frac{{YE + YA}}{2}\right)\)

Plugging in the values of the endpoints into the midpoint formula, we obtain:

M = \(\left(\frac{{XE + XA}}{2}, \frac{{YE + YA}}{2}\right)\)

Therefore, the correct answer is Option A: \(\left(\frac{{2XE + XA}}{2}, \frac{{2YE + YA}}{2}\right)\), which simplifies to the midpoint formula given above.