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

- 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:} \\ ((x_1+x_2)/(2),(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)=((1+(-5))/(2),(8+(-2))/(2)) \\ \\ Mid(AB)=(-2,3) \end{gathered}`

Distance:

`\begin{gathered} \text{ The distance between two points is:} \\ D_(AB)=√((y_2-y_1)^2+(x_2-x_1)^2) \\ \\ D_(AB)=√((8-(-2)^2+(1-(5))^2) \\ D_(AB)=√(10^2+6^2)=√(100+36) \\ D_(AB)=√(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=(y_2-y_1)/(x_2-x_1) \\ \\ m=(8-(-2))/(1-(-5))=(10)/(6)=(5)/(3) \end{gathered}`