Question

What is the midpoint of EF, if E has the coordinates of (2,4) and F has a coordinate of (6,8)

Answer 1

To answer this question, we need to remember that the midpoint formula is given by:

`\begin{gathered} m_x=(x_1+x_2)/(2) \\ m_y=(y_1+y_2)/(2) \end{gathered}`

That is, we can find both coordinates for the midpoint of the segment EF applying it.

We know that the coordinates of E, and F are:

• E(2, 4)

,

• F(6, 8)

Then we can identify them as follows:

• E(2, 4) ---> x1 = 2, y1 = 4

,

• F(6, 8) ---> x2 = 6, y2 = 8

Therefore, we have that the midpoint of the segment EF is:

The x-coordinate is:

`\begin{gathered} m_x=(x_1+x_2)/(2) \\ m_x=(2+6)/(2)=(8)/(2)=4 \\ m_x=4 \end{gathered}`

And the y-coordinate is:

`\begin{gathered} m_y=(y_1+y_2)/(2) \\ m_y=(4+8)/(2)=(12)/(2)=6 \\ m_y=6 \end{gathered}`

In summary, therefore, the midpoint of the segment EF is (4, 6).

We can check this if we see the following graph (showing only the extreme points and the midpoint):