Question

How do you find the midpoint of the line segment joining (3, 5) and (-2, -4)?

Answer 1

Hint: The midpoint is halfway between the two endpoints. That means its x value is halfway between the two x values, and its y value is halfway between the two y values.
To calculate the midpoint of the line segment:
Add both ‘x’ coordinates and then divide by 2
Add both ‘y’ coordinates and then divide by 2
The formula to find the midpoint of the line segment joining $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$. The midpoint is denoted by M.
$M = \left( {\dfrac{{{x_1} + {x_2}}}{2},\dfrac{{{y_1} + {y_2}}}{2}} \right)$

Complete step-by-step answer:
In this question, two points of the line are given and we want to find the midpoint.
So, we will use the formula of midpoint.
$M = \left( {\dfrac{{{x_1} + {x_2}}}{2},\dfrac{{{y_1} + {y_2}}}{2}} \right)$
Here, the two points of the line segment are (3, 5) and (-2, -4).
Let us compare these two points with $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$.
Therefore,
The value of ${x_1}$is 3.
The value of ${y_1}$ is 5.
The value of ${x_2}$ is -2.
The value of ${y_2}$ is -4.
Let us substitute all the values in the midpoint formula.
 $ \Rightarrow M = \left( {\dfrac{{3 + \left( { - 2} \right)}}{2},\dfrac{{5 + \left( { - 4} \right)}}{2}} \right)$
Simplify the above expression.
$ \Rightarrow M = \left( {\dfrac{{3 - 2}}{2},\dfrac{{5 - 4}}{2}} \right)$
Now, apply subtraction to the numerator.
$ \Rightarrow M = \left( {\dfrac{1}{2},\dfrac{1}{2}} \right)$
Hence, the midpoint of the line segment is $\left( {\dfrac{1}{2},\dfrac{1}{2}} \right)$.

Note:
As we know, a line segment is a part of a line that is bound by two distinct points, which are called the endpoints of the line segment. Point M is the midpoint of the line segment if it is an element of the segment and divides it into two congruent segments. Each segment between midpoint M and an endpoint has an equal length. It is often said that point M bisects the segment. In other words, the midpoint is a center or midpoint of a line segment. Any line segment has a unique midpoint.