Point
\[\blue{A}\] is at
\[\blue{(3, -8)}\] and point
\[\purple{M}\] is at
\[\purple{(5, -2.5)}\].
Point
\[\purple{M}\] is the midpoint of point
\[\blue{A}\] and point
\[\green{B}\].
What are the coordinates of point
\[\green{B}\]?
Since point $\purple{M}$ is the midpoint of points $\blue{A}$ and $\green{B}$, we can find the coordinates of point $\green{B}$ by finding the average of the coordinates of points $\blue{A}$ and $\purple{M}$.
The $x$-coordinate of point $\green{B}$ is the average of the $x$-coordinates of points $\blue{A}$ and $\purple{M}$: \[\frac{3+5}{2}=4.\]
The $y$-coordinate of point $\green{B}$ is the average of the $y$-coordinates of points $\blue{A}$ and $\purple{M}$: \[\frac{(-8)+(-2.5)}{2}=-5.25.\]
Therefore, the coordinates of point $\green{B}$ are $\boxed{(4, -5.25)}$.
To find the coordinates of point \(\green{B}\), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of two points, \((x_1, y_1)\) and \((x_2, y_2)\), is given by:
\[
\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)
\]
Here, we have the coordinates of point \(\blue{A}\) as \(\blue{(3, -8)}\) and the coordinates of point \(\purple{M}\) as \(\purple{(5, -2.5)}\). Let's substitute these values into the midpoint formula:
\[
\left(\frac{{3 + x_2}}{2}, \frac{{-8 + y_2}}{2}\right) = \purple{(5, -2.5)}
\]
By comparing the x-coordinates and y-coordinates separately, we can solve for \(x_2\) and \(y_2\):
For the x-coordinate:
\(\frac{{3 + x_2}}{2} = 5\)
\(\frac{{3 + x_2}}{2} \times 2 = 5 \times 2\)
\(3 + x_2 = 10\)
\(x_2 = 10 - 3\)
\(x_2 = 7\)
For the y-coordinate:
\(\frac{{-8 + y_2}}{2} = -2.5\)
\(\frac{{-8 + y_2}}{2} \times 2 = -2.5 \times 2\)
\(-8 + y_2 = -5\)
\(y_2 = -5 + 8\)
\(y_2 = 3\)
Hence, the coordinates of point \(\green{B}\) are \(\green{(7, 3)}\).
To find the coordinates of point \[\green{B}\], we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points \((x_1, y_1)\) and \((x_2, y_2)\) are given by \(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\).
In this case, we are given that point \[\purple{M}\] is the midpoint between point \[\blue{A}\] and point \[\green{B}\], so we can use the midpoint formula with the known coordinates of \[\purple{M}\] and \[\blue{A}\], which are \(\purple{(5, -2.5)}\) and \(\blue{(3, -8)}\), respectively.
Let's apply the midpoint formula:
\[
\begin{align*}
x &= \frac{{x_1 + x_2}}{2} \\
&= \frac{{5 + 3}}{2} \\
&= \frac{8}{2} \\
&= 4
\end{align*}
\]
\[
\begin{align*}
y &= \frac{{y_1 + y_2}}{2} \\
&= \frac{{-2.5 + (-8)}}{2} \\
&= \frac{-10.5}{2} \\
&= -5.25
\end{align*}
\]
Therefore, the coordinates of point \[\green{B}\] are \(\green{(4, -5.25)}\).