To find the coordinates of point $\green{B}$, we can use the midpoint formula. The formula states that if the coordinates of the two endpoints of a segment are $(x_1, y_1)$ and $(x_2, y_2)$, then the coordinates of the midpoint are $\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)$.
In this problem, the two endpoints of the segment are $\blue{A}$ at $(-2, -7)$ and $\green{B}$ at $(x, y)$. The midpoint $\purple{M}$ is given to be $(2.5, -1.5)$. Using the midpoint formula, we have \[(2.5,-1.5) = \left(\dfrac{x + (-2)}{2}, \dfrac{y + (-7)}{2}\right).\] Simplifying this equation gives us \[(2.5, -1.5) = \left(\dfrac{x - 2}{2}, \dfrac{y - 7}{2}\right).\] We can solve this equation to find that $x-2=5$ and $y-7=-3$. Therefore, $x=7$ and $y=4$.
Hence the coordinates of point $\green{B}$ are $\boxed{(7, 4)}$.
Point
\[\blue{A}\] is at
\[\blue{(-2, -7)}\] and point
\[\purple{M}\] is at
\[\purple{(2.5, -1.5)}\].
Point
\[\purple{M}\] is the midpoint of point
\[\blue{A}\] and point
\[\green{B}\].
What are the coordinates of point
\[\green{B}\]?
1 answer
1 answer