Question

How do you find the midpoint of $\left( {5,2} \right)$, $\left( {3, - 6} \right)$?

Answer 1

Hint: This problem deals with finding the midpoint between the two given endpoints, and dividing the result by 2. The distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates. If the endpoints of a line segment is $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$, then the midpoint of the line segment has the coordinates:
$ \Rightarrow \left( {\dfrac{{{x_1} + {x_2}}}{2},\dfrac{{{y_1} + {y_2}}}{2}} \right)$

Complete step-by-step solution:
Given two coordinate points from a Cartesian coordinates plane.
The points are given by $\left( {5,2} \right)$ and $\left( {3, - 6} \right)$.
Consider the point $\left( {5,2} \right)$, in this point both the x and y coordinates are positive, which means that this point is in the first quadrant.
Now consider the second point which is $\left( {3, - 6} \right)$, in this point the x coordinate is positive but whereas the y coordinate is negative, which means that this point is in the fourth quadrant.
Now these points happen to be the end points of a line, so finding the midpoint of these two points.
Now to find the midpoint of the two above given points, we have to just apply the midpoint formula.
Let $\left( {{x_1},{y_1}} \right) = \left( {5,2} \right)$ and $\left( {{x_2},{y_2}} \right) = \left( {3, - 6} \right)$
The midpoint is given by:
$ \Rightarrow \left( {\dfrac{{5 + 3}}{2},\dfrac{{2 + \left( { - 6} \right)}}{2}} \right) = \left( {\dfrac{8}{2},\dfrac{{ - 4}}{2}} \right)$
$ \Rightarrow \left( {4, - 2} \right)$

The midpoint of the points $\left( {5,2} \right)$ and $\left( {3, - 6} \right)$ is $\left( {4, - 2} \right)$

Note: Please note that if you want to make sure whether the obtained point is the correct midpoint, then just calculate the distance between the obtained midpoint to any one of the given points, this distance should be equal to the half of the distance between the two given points, then this is the correct midpoint.