Question

for this pair of points, find the distance between them either exactly or rounded to 3 decimal places. also find each coordinate of the midpoint of the line segment joining them exactly. (-4,3),(-5,-3) distance: midpoint: () question help: video ebook written example

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-4,y_1 = 3,x_2=-5,y_2=-3$.
\[

$$\begin{align*} d&=\sqrt{(-5-(-4))^2+(-3 - 3)^2}\\ &=\sqrt{(-5 + 4)^2+(-6)^2}\\ &=\sqrt{(-1)^2+36}\\ &=\sqrt{1 + 36}\\ &=\sqrt{37}\approx6.083 \end{align*}$$

\]

Step2: Recall mid - point formula

The mid - point $M$ of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ has coordinates $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
\[

$$\begin{align*} x_{mid}&=\frac{-4+( - 5)}{2}=\frac{-4-5}{2}=-\frac{9}{2}=-4.5\\ y_{mid}&=\frac{3+( - 3)}{2}=\frac{3 - 3}{2}=0 \end{align*}$$

\]

Answer:

Distance: $6.083$
Midpoint: $(-4.5,0)$