Question

In the standard (x, y) coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (−3, 0) and (7, 4)?
A. (2, 2)
B. (2, 3)
C. (5, 2)
D. (5, 4)

Answer 1

Hint: Here, we will use the midpoint formula of coordinate geometry in (x, y) plane, to find the midpoint of the line of given endpoint. Because using the midpoint formula, we can easily find the midpoint coordinates by doing simple calculations. We can also cross check our answer by using a graphical method for finding the same.

Complete step by step answer:
The endpoints of the given line segment are (−3, 0) and (7, 4).
Let A (−3, 0) and B (7, 4).
Midpoint of AB = \[\left( {\dfrac{{\left( { - 3 + 7} \right)}}{2},\dfrac{{\left( {0 + 4} \right)}}{2}} \right)\] [Using midpoint formula]
[Midpoint Formula: Midpoint of a line with coordinates of endpoint as $({x_1},{y_1})$ and $({x_2},{y_2})$is given as\[\left( {\dfrac{{\left( {{x_1} + {x_2}} \right)}}{2},\dfrac{{\left( {{y_1} + {y_2}} \right)}}{2}} \right)\]]
Midpoint of AB = \[\left( {\dfrac{4}{2},\dfrac{4}{2}} \right) = \left( {2,2} \right)\]
The coordinates of the midpoint of a line segment whose endpoints are (−3, 0) and (7, 4) is (2, 2).
Hence, the correct option is (A).

Note: In these types of questions, we should directly use the midpoint formula (i.e. algebraic method). We can also find the midpoint using a graphical method. By graphical method, plot the given points and draw the line by joining them. Then mark the midpoint using a protractor (i.e. draw a perpendicular bisector of the line drawn) and deduce the midpoint from the graph. But we should use graphical methods for easily marking able points because for points like $\sqrt {2,} \sqrt 5 $ or any point in fraction it will not be easy to plot it and also midpoint cannot be deduced from the graph significantly. Always keep in mind that algebraic method is a simpler way to find as compared to graphical method, for simple coordinates as well as for coordinates involving fractions and square roots.