Question

Find the coordinates of the midpoint of the line segment joining the points (2,3) and (4,7).

Answer 1

Hint: We will use the midpoint formula to solve this question. And it is given as, $ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $ where $ \left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right) $ are the two given points and (x,y) is the coordinate of the midpoint of the line segment joining the points $ \left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right) $ .

Complete step-by-step answer:
It is given in the question that we have to find the coordinates of the mid-point of the line segment joining the points (2,3) and (4,7).
So, let us consider the coordinates of the first point, let us say point A as $ \left( {{x}_{1}},{{y}_{1}} \right)=\left( 2,3 \right) $ and the coordinates of the second point, say point B as $ \left( {{x}_{2}},{{y}_{2}} \right)=\left( 4,7 \right) $ .
Now, we know that in order to find the midpoint of line segment joining two points, A and B, we have a formula, that is, $ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $ where $ \left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right) $ are the two points, A and B, and (x,y) is the coordinate of the midpoint, say M, of the line segment joining the points A and B, which are, $ \left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right) $ .

So, on substituting the values of $ {{x}_{1}}=2,{{x}_{2}}=4,{{y}_{1}}=3,{{y}_{2}}=7 $ in the midpoint formula, we will get the x-coordinate of the midpoint as,
 $ \begin{align}
  & x=\dfrac{2+4}{2} \\
 & x=\dfrac{6}{2} \\
 & x=3 \\
\end{align} $
And the y-coordinate of the midpoint will be as follows,
 $ \begin{align}
  & y=\dfrac{3+7}{2} \\
 & y=\dfrac{10}{2} \\
 & y=5 \\
\end{align} $
Thus, we have got the x-coordinate of the mid-point as 3 and the y-coordinate of the midpoint as 5.
Therefore, the coordinates of the midpoint of the line segment joining the points (2,3) and (4,7) is (3,5).

Note: This is a direct question where we have been asked to find the midpoint of a line segment joining two points. But still some students make mistakes. The possible mistake that the students can make in this question is by writing the wrong formula of the midpoint. They may write it as, $ x=\dfrac{{{x}_{2}}-{{x}_{1}}}{2},y=\dfrac{{{y}_{2}}-{{y}_{1}}}{2} $ , which is wrong. So, the students must remember the correct midpoint formula, that is, $ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $ .