Point
\[\blue{A}\] is at
\[\blue{(-1, 8)}\] and point
\[\purple{M}\] is at
\[\purple{(3, 5.5)}\].
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 point \(\blue{A}\) and point \(\green{B}\), we can find the coordinates of point \(\green{B}\) by doubling the coordinates of point \(\purple{M}\) and then subtracting the coordinates of point \(\blue{A}\).
So, let's double the x-coordinate of point \(\purple{M}\) and subtract the x-coordinate of point \(\blue{A}\):
\(2 \cdot 3 - (-1) = 6 + 1 = \boxed{7}\)
Next, let's double the y-coordinate of point \(\purple{M}\) and subtract the y-coordinate of point \(\blue{A}\):
\(2 \cdot 5.5 - 8 = 11 - 8 = \boxed{3}\)
Therefore, the coordinates of point \(\green{B}\) are \(\boxed{(7, 3)}\).
To find the coordinates of point \(\green{B}\), we can use the midpoint formula. The midpoint formula states that if the midpoint \(\purple{M}\) is \((x_{1}, y_{1})\) and one endpoint \(\blue{A}\) is \((x_{2}, y_{2})\), then the coordinates of the other endpoint \(\green{B}\) are \((2x_{1} - x_{2}, 2y_{1} - y_{2})\).
Given that point \(\purple{M}\) is \((3, 5.5)\) and point \(\blue{A}\) is \((-1, 8)\), we can substitute these values into the midpoint formula:
\[
\begin{align*}
x_{1} &= 3 \\
y_{1} &= 5.5 \\
x_{2} &= -1 \\
y_{2} &= 8
\end{align*}
\]
Using the formula, we can find the coordinates of point \(\green{B}\) as:
\[
\begin{align*}
x_{\green{B}} &= 2x_{1} - x_{2} = 2(3) - (-1) = 6 + 1 = 7 \\
y_{\green{B}} &= 2y_{1} - y_{2} = 2(5.5) - 8 = 11 - 8 = 3
\end{align*}
\]
Therefore, the coordinates of point \(\green{B}\) are \(\green{(7, 3)}\).
To find the coordinates of point \[\green{B}\], we need to determine the midpoint of points \[\blue{A}\] and \[\green{B}\].
Given that point \[\purple{M}\] is the midpoint of point \[\blue{A}\] and point \[\green{B}\], we can use the midpoint formula to find the coordinates of \[\green{B}\].
The midpoint formula states that the coordinates of the midpoint \(\purple{(x_m, y_m)}\) between two points \(\blue{(x_1, y_1)}\) and \(\green{(x_2, y_2)}\) are:
\[
x_m = \frac{{x_1 + x_2}}{2} \quad \text{and} \quad y_m = \frac{{y_1 + y_2}}{2}
\]
In this case, we know the coordinates of point \[\blue{A}\] as \[\blue{(-1, 8)}\] and the coordinates of point \[\purple{M}\] as \[\purple{(3, 5.5)}\].
Let's substitute these values into the midpoint formula to find the coordinates of point \[\green{B}\]:
\[
x_m = \frac{{(-1) + x_2}}{2} \quad \implies \quad -1 + x_2 = 2x_m
\]
\[
y_m = \frac{{8 + y_2}}{2} \quad \implies \quad 8 + y_2 = 2y_m
\]
Plugging in the known values, we have:
\[
-1 + x_2 = 2(3) \quad \implies \quad -1 + x_2 = 6
\]
\[
8 + y_2 = 2(5.5) \quad \implies \quad 8 + y_2 = 11
\]
Solving for \(x_2\) and \(y_2\):
\[
x_2 = 6 + 1 \quad \implies \quad x_2 = 7
\]
\[
y_2 = 11 - 8 \quad \implies \quad y_2 = 3
\]
Therefore, the coordinates of point \[\green{B}\] are \[\green{(7, 3)}\].