Question

The midpoint of the line segment with endpoints $\left( { - 6,4} \right)\;{\text{and}}\;\left( {8,2} \right)$ is
A) $\left( {3,1} \right)$
B) $\left( {1,3} \right)$
C) $\left( {2,6} \right)$
D) $\left( {3,3} \right)$

Answer 1

Hint : This is a direct question which is based on the formula of the midpoint of the line segment.
We should know the formula of midpoint of a line segment,
That is $\left( {x,y} \right) = \left( {\dfrac{{{x_1} + {x_2}}}{2},\;\dfrac{{{y_1} + {y_2}}}{2}} \right)$
Where $\left( {x,y} \right)$ is the midpoint of the segment $\left( {{x_1}\;{y_1}} \right)\;{\text{and}}\;\left( {{x_{{2_1}}}{y_2}} \right)$ are the given two points of the line segment.

Complete step-by-step answer:
According to the given question,
$\left( {{x_1},{y_1}} \right)\; = \;\left( { - 6,4} \right)\;\;{\text{and}}\;\left( {{x_2},{y_2}} \right) = \left( {8,2} \right)$
Substituting these points in the above formula we, get,
$\left( {x,4} \right) = \left( { - \dfrac{{6 + 8}}{2},\dfrac{{4 + 2}}{2}} \right)$
     $ = \left( {\dfrac{{ + {}{2}}}{{{2}}},\dfrac{{{6}}}{{{2}}}} \right)$
$\left( {{x_1}4} \right) = \left( {1,3} \right)$

Therefore, A is the correct answer.

Note : These types of question, formulas are the most important. Knowing the formulas makes the question very easy to solve . Midpoint divides the line into two equal halves.