Point
\[\blue{A}\] is at
\[\blue{(3, 4)}\] and point
\[\green{B}\] is at
\[\green{(8, -4)}\].
What is the midpoint of line segment
\[\overline{AB}\]?
To find the midpoint of line segment $\overline{AB}$, we can take the average of the coordinates of points $A$ and $B$. Let's call the midpoint $M$.
To find the $x$-coordinate of $M$, we average the $x$-coordinates of $A$ and $B$. The $x$-coordinate of $A$ is $3$ and the $x$-coordinate of $B$ is $8$, so the $x$-coordinate of $M$ is $\frac{3+8}{2} = \frac{11}{2}$.
To find the $y$-coordinate of $M$, we average the $y$-coordinates of $A$ and $B$. The $y$-coordinate of $A$ is $4$ and the $y$-coordinate of $B$ is $-4$, so the $y$-coordinate of $M$ is $\frac{4+(-4)}{2} = 0$.
Therefore, the midpoint $M$ of line segment $\overline{AB}$ is $\left(\frac{11}{2}, 0\right)$.
To find the midpoint of a line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
In this case, the coordinates of point A are (3, 4) and the coordinates of point B are (8, -4).
So, applying the midpoint formula:
Midpoint = ( (3 + 8) / 2 , (4 + (-4)) / 2 )
= ( 11 / 2 , 0 / 2 )
= ( 5.5 , 0 )
Therefore, the midpoint of line segment AB is (5.5, 0).
To find the midpoint of a line segment, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint, denoted as \((m_x, m_y)\), of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[m_x = \frac{{x_1 + x_2}}{2}\]
\[m_y = \frac{{y_1 + y_2}}{2}\]
Given that point \(\blue{A}\) is at \(\blue{(3, 4)}\) and point \(\green{B}\) is at \(\green{(8, -4)}\), we can use the midpoint formula to find the coordinates of the midpoint of line segment \(\overline{AB}\).
Substituting the given coordinates into the midpoint formula, we have:
\[m_x = \frac{{3 + 8}}{2} = \frac{{11}}{2} = 5.5\]
\[m_y = \frac{{4 + (-4)}}{2} = \frac{{0}}{2} = 0\]
Therefore, the midpoint of line segment \(\overline{AB}\) is \((5.5, 0)\).