Question

Given point A(1, 8) and point B(-5,-2). Find the following: a ) The coordinates of the midpoint of segment ABWrite your answer in this form: (x, y) (7 points) b ) Using the distance formula, find the length of segment AB. Round to the nearest hundredth. ( 7 points) ) Find the slope of segment AB. (if your answer is a fraction, use the symbol) (7 points)

Answer 1

Solution

- We are given the points:

$\begin{gathered} A=(1,8) \\ B=(-5,-2) \end{gathered}$

Midpoint:

$\begin{gathered} \text{ The formula for finding the midpoint is:} \\ (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ where, \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points} \\ \\ \text{ Thus, we have:} \\ Mid(AB)=(\frac{1+(-5)}{2},\frac{8+(-2)}{2}) \\ \\ Mid(AB)=(-2,3) \end{gathered}$

Distance:

$\begin{gathered} \text{ The distance between two points is:} \\ D_{AB}=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ D_{AB}=\sqrt{(8-(-2)^2+(1-(5))^2} \\ D_{AB}=\sqrt{10^2+6^2}=\sqrt{100+36} \\ D_{AB}=\sqrt{136}\approx11.66\text{ \lparen To the nearest hundredth\rparen} \\ \end{gathered}$

Slope:

$\begin{gathered} \text{ The formula for the slope of the line connecting two points A and B} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{8-(-2)}{1-(-5)}=\frac{10}{6}=\frac{5}{3} \end{gathered}$