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
[tex]\text{if P1(x}_1,y_1)\text{ and P2(x}_2,y_2)[/tex]
the distance between P1 and P2 is
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2_{}_{}} \\ \end{gathered}[/tex]
Step 1
put the values into the equation
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2_{}} \\ d=\sqrt{(-1-(5))^2+(-5-(-5))^2_{}} \\ d=\sqrt{(-6)^2+(0)^2} \\ d=\sqrt{36} \\ d=6 \end{gathered}[/tex]
so, the length of AB is 6 units
10. What is the midpoint of CD? Justify your answer.
[tex]\begin{gathered} \text{let P1(x}_1,y_1)andP2(x_2,y_2) \\ \end{gathered}[/tex]
the midpoint of P1 and P2 is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
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)
[tex]\begin{gathered} M=(\frac{-3+6}{2},\frac{4+3}{2}) \\ M=(\frac{3}{2},\frac{7}{2}) \\ M=(1.5,\text{ 3.5)} \end{gathered}[/tex]
so, the midpoint is (1.5,3.5)
I hope this helps you
