Q23. - Algebra 1

Question

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

$\mathbf{(}\mathbf{-}\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{8}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{10}\mathbf{,}\mathbf{-}\mathbf{6}\mathbf{)}$

Step-by-Step Solution

Answer

The coordinates of the midpoint of the segment with the given endpoints is $\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{7}\mathbf{)}$.

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:

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

Where$(x,y)$is the midpoint.

Step 2. Calculate the distance.

The two points which is given are$(-4,-8)$and$(10,-6)$.

Substitute$(-4,-8)$as$(x_1,y_1)$and$(10,-6)$as$(x_2,y_2)$in (1) to calculate the distance.

 $\begin{array}{c}(x,y)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{-4+10}{2},\frac{-8+(-6)}{2}\right)\\ =\left(\frac{6}{2},\frac{-8-6}{2}\right)\\ =\left(\frac{6}{2},\frac{-14}{2}\right)\\ =(3,-7)\end{array}$

Step 3. State the conclusion.

Therefore, midpoint of the segment with the endpoints $(-4,-8)$ and $(10,-6)$ is $(3,-7)$.