Question

2. FR has a midpoint M. Use the given information to findthe missing endpoint. F(-2,3) and M(3,0)

Answer 1

We know that

• M is the midpoint of FR.

,

• F(-2,3) and M(3,0).

The midpoint formula is

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where (x_1, y_1) represents point F and (x_2, y_2) represents point R (the missing point). So, our job is to find (x_2, y_2). Let's replace the information we have so far

$(3,0)=(\frac{-2+x_2}{2},\frac{3+y_2}{2})$

Let's separate the coordinates, that is, the horizontal coordinate 3 belongs to the horizontal coordinate on the other side of the equation, and the vertical coordinate 0 belongs to the vertical coordinate on the other side of the equation. So, we can rewrite the equation we have as two equations.

$\begin{gathered} 3=\frac{-2+x_2}{2} \\ 0=\frac{3+y_2}{2} \end{gathered}$

The first equation will give us the horizontal coordinate of point R, and the second equation will give us the vertical coordinate of point R. Let's solve both of them

$\begin{gathered} 3=\frac{-2+x_2}{2}\to6=-2+x_2\to x_2=6+2\to x_2=8 \\ 0=\frac{3+y_2}{2}\to0=3+y_2\to y_2=-3 \end{gathered}$

Therefore, the missing endpoint is (8,-3).

The image below shows all three points.