Question

use the number line to find the coordinate of the midpoint of each segment.
e f g h j k l
-6 -4 -2 0 2 4 6 8 10

1. (overline{fk}) 8. (overline{hk}) 9. (overline{ef})
2. (overline{fg}) 11. (overline{jl}) 12. (overline{el})

use tools use the number line to find the coordinate of the midpoint of each segment.
a b c d e
-6 -4 -2 0 2 4 6 8 10 12

1. (overline{de}) 14. (overline{bc})
2. (overline{bd}) 16. (overline{ad})

Explanation:

Step1: Recall mid - point formula on number line

The mid - point of a line segment with endpoints $x_1$ and $x_2$ on a number line is given by $\frac{x_1 + x_2}{2}$.

Step2: Solve for $\overline{FK}$

The coordinate of $F=-2$ and the coordinate of $K = 9$. So the mid - point is $\frac{-2 + 9}{2}=\frac{7}{2}=3.5$.

Step3: Solve for $\overline{HK}$

The coordinate of $H = 3$ and the coordinate of $K = 9$. So the mid - point is $\frac{3+9}{2}=\frac{12}{2}=6$.

Step4: Solve for $\overline{EF}$

The coordinate of $E=-6$ and the coordinate of $F=-2$. So the mid - point is $\frac{-6+( - 2)}{2}=\frac{-8}{2}=-4$.

Step5: Solve for $\overline{FG}$

The coordinate of $F=-2$ and the coordinate of $G = 0$. So the mid - point is $\frac{-2 + 0}{2}=-1$.

Step6: Solve for $\overline{JL}$

The coordinate of $J = 6$ and the coordinate of $L = 10$. So the mid - point is $\frac{6 + 10}{2}=\frac{16}{2}=8$.

Step7: Solve for $\overline{EL}$

The coordinate of $E=-6$ and the coordinate of $L = 10$. So the mid - point is $\frac{-6+10}{2}=\frac{4}{2}=2$.

Step8: Solve for $\overline{DE}$

The coordinate of $D = 6$ and the coordinate of $E = 10$. So the mid - point is $\frac{6 + 10}{2}=8$.

Step9: Solve for $\overline{BC}$

The coordinate of $B=-2$ and the coordinate of $C = 2$. So the mid - point is $\frac{-2 + 2}{2}=0$.

Step10: Solve for $\overline{BD}$

The coordinate of $B=-2$ and the coordinate of $D = 6$. So the mid - point is $\frac{-2+6}{2}=\frac{4}{2}=2$.

Step11: Solve for $\overline{AD}$

The coordinate of $A=-4$ and the coordinate of $D = 6$. So the mid - point is $\frac{-4 + 6}{2}=\frac{2}{2}=1$.

Answer:

1. $3.5$
2. $6$
3. $-4$
4. $-1$
5. $8$
6. $2$
7. $8$
8. $0$
9. $2$
10. $1$