Question

For 9-10, use the graph below. 9. What is the length of AB? Explain your reasoning.10. What is the midpoint of CD? Justify your answer.Please show all work and not just answer.

Answer 1

9. What is the length of AB? Explain your reasoning.

Let

A(-5,5)

B(-5,-1)

to find the length you can use the distance between two points formula

`\text{if P1(x}_1,y_1)\text{ and P2(x}_2,y_2)`

the distance between P1 and P2 is

`\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2_{}_{}} \\ \end{gathered}`

Step 1

put the values into the equation

`\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2_{}} \\ d=\sqrt{(-1-(5))^2+(-5-(-5))^2_{}} \\ d=√((-6)^2+(0)^2) \\ d=√(36) \\ d=6 \end{gathered}`

so, the length of AB is 6 units

10. What is the midpoint of CD? Justify your answer.



`\begin{gathered} \text{let P1(x}_1,y_1)andP2(x_2,y_2) \\ \end{gathered}`

the midpoint of P1 and P2 is

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Step 2

Put the values of C and D into the equation

let P1=C and P2=D

C(-3,4) and D(6,3)

`\begin{gathered} M=((-3+6)/(2),(4+3)/(2)) \\ M=((3)/(2),(7)/(2)) \\ M=(1.5,\text{ 3.5)} \end{gathered}`

so, the midpoint is (1.5,3.5)

I hope this helps you