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=((x_1+x_2)/(2),(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)=((-2+x_2)/(2),(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=(-2+x_2)/(2) \\ 0=(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=(-2+x_2)/(2)\to6=-2+x_2\to x_2=6+2\to x_2=8 \\ 0=(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.