Question

09/03 - segment bisector practice l (updated)
possible points: 5.4
using the figure, answer the following questions.

1. name the mid - point of aq.
2. what is the coordinate of the mid - point of ws?
3. what is the coordinate of the mid - point of sb?
4. the coordinate of the mid - point ar is - 3. what is the coordinate point of r?
5. the coordinate of the mid - point of st is 4. what is the coordinate of point t?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points with coordinates $x_1$ and $x_2$ on a number line is $M=\frac{x_1 + x_2}{2}$.

Step2: Find mid - point of $\overline{AQ}$

The coordinate of $A$ is $0$ and the coordinate of $Q$ is $4$. Using the mid - point formula $M=\frac{0 + 4}{2}=2$, so the mid - point is $S$.

Step3: Find mid - point of $\overline{WS}$

The coordinate of $W$ is $-8$ and the coordinate of $S$ is $2$. Then $M=\frac{-8 + 2}{2}=\frac{-6}{2}=-3$.

Step4: Find mid - point of $\overline{SB}$

The coordinate of $S$ is $2$ and the coordinate of $B$ is $8$. So $M=\frac{2+8}{2}=\frac{10}{2}=5$.

Step5: Find coordinate of $R$ given mid - point of $\overline{AR}$

Let the coordinate of $R$ be $x$. The coordinate of $A$ is $0$ and the mid - point of $\overline{AR}$ is $-3$. Using the mid - point formula $\frac{0 + x}{2}=-3$. Multiply both sides by $2$: $0 + x=-6$, so $x=-6$.

Step6: Find coordinate of $T$ given mid - point of $\overline{ST}$

Let the coordinate of $T$ be $y$. The coordinate of $S$ is $2$ and the mid - point of $\overline{ST}$ is $4$. Using the mid - point formula $\frac{2 + y}{2}=4$. Multiply both sides by $2$: $2 + y = 8$, then $y=6$.

Answer:

1. $S$
2. $-3$
3. $5$
4. $-6$
5. $6$