Question

What are the coordinates of the midpoint of EF if point E is located at (–12, 5) and point F is located at (7, –9)?

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ E(\stackrel{x_1}{-12}~,~\stackrel{y_1}{5})\qquad F(\stackrel{x_2}{7}~,~\stackrel{y_2}{-9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7-12}{2}~~,~~\cfrac{-9+5}{2} \right)\implies \left( \cfrac{-5}{2}~~,~~\cfrac{-4}{2} \right)\implies \left( -2(1)/(2)~~,~-2 \right)`

Answer 2

`\left((-5)/(2),-2\right)`

Explanation:

It is given that point E is located at (–12, 5) and point F is located at (7, –9).

We need to find the coordinates of the midpoint of EF.

Formula for midpoint:

`Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

Substitute the given values in the above formula.

`Midpoint=\left((-12+7)/(2),(5-9)/(2)\right)`

On simplification, we get

`Midpoint=\left((-5)/(2),(-4)/(2)\right)`

`Midpoint=\left((-5)/(2),-2\right)`

Therefore, the midpoint is
`\left((-5)/(2),-2\right)`.