Q21. - Algebra 1

Question

Find the coordinates of the midpoint of the segment with the given endpoints.

$\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{3}\mathbf{)}$

Step-by-Step Solution

Answer

The coordinates of the midpoint of the segment with the given endpoints is $\left(-\frac{{\displaystyle 5}}{{\displaystyle 2}},\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)$.

Step 1. State the concept of ‘midpoint of a segment in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_1,y_1)$ and $(x_2,y_2)$.

The midpoint of the segment with endpoints is given as:

 $(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \dots \left(1\right)$

Where $(x,y)$ is the midpoint.

Step 2. Calculate the distance.

The two points which is given are $(-3,4)$ and $(-2,-3)$.

Substitute $(-3,4)$ as $(x_1,y_1)$ and $(-2,-3)$ as $(x_2,y_2)$ in $\left(1\right)$ to calculate the distance.

  $\begin{array}{l}(x,y)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{-3+(-2)}{2},\frac{4+(-3)}{2}\right)\\ =\left(\frac{-3-2}{2},\frac{4-3}{2}\right)\\ =\left(\frac{-5}{2},\frac{1}{2}\right)\\ =\left(-\frac{5}{2},\frac{1}{2}\right)\end{array}$

Step 3. State the conclusion.

Therefore, midpoint of the segment with the endpoints $(-3,4)$ and $(-2,-3)$ is $\left(-\frac{{\displaystyle 5}}{{\displaystyle 2}},\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)$.