Q1. - Precalculus Enhanced with Graphing Utilities

Question

Suppose the points $\left(-2,-3\right)$ and $\left(4,5\right)$ are the endpoints of a line segment.

(a) Find the distance between the two points.

(b) Find the midpoint of the line segment connecting the two points.

(a) Find the distance between the two points.

(b) Find the midpoint of the line segment connecting the

two points.

Step-by-Step Solution

Answer

The distance between two points is $10$ and midpoints is $\left(1,1\right)$.

Step 1. Given information.

Consider the given information that the endpoints of a line segment are $\left(-2,-3\right)$ and $\left(4,5\right)$. 

Step 2. Formula used .

The formula for finding distance between two points is given by $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$and formula for finding mid points between two points is given by $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 3. Using distance formula to calculate distance .

Substitute value of $x_1=-2 , x_2=4$and $y_1=-3 , y_2=5$

$$\begin{gathered} d=\sqrt{{\left(4+2\right)}^2+{\left(5+3\right)}^2} \\ d=\sqrt{100} \\ d=10 \end{gathered}$$

Step 4. Using midpoints formula to calculate midpoints.

Substitute the values of $x_1, x_2$and $y_1 ,y_2$ .

$\left(\frac{-2+4}{2}, \frac{-3+5}{2}\right)$ therefore the midpoint is  $\left(1,1\right)$.