Q9. - Geometry

Question

For the following figure, find each distance.

a. $RS$

b. $RQ$

c. $PT$

Step-by-Step Solution

Answer

a. The distance of $RS$ is 1 unit.

b. The distance of $RQ$ is 1 unit.

c. The distance of $PT$ is 4 unit.

Part a. Step 1. Check the number line.

Consider the number line.

Part a. Step 2. Apply the concept.

On a number line, the coordinate of a point is the value that the point represents. 

 

The ruler postulate states that distance between two points equals the absolute value of the difference between their coordinates.

Part a. Step 3. Step description.

From the number line, the coordinate of point $R$ is 0 and the coordinate of point $S$ is 1.

 

Calculate the distance of $RS$ as follows:

$$\begin{gathered} RS=|1-0| \\ =1 \end{gathered}$$ 

 

Thus, the distance of $RS$ is 1 unit.

Part b. Step 1. Check the number line.

Consider the number line.

Part b. Step 2. Apply the concept.

On a number line, the coordinate of a point is the value that the point represents. 

 

The ruler postulate states that distance between two points equals the absolute value of the difference between their coordinates.

Part b. Step 3. Step description.

From the number line, the coordinate of point $R$ is 0 and the coordinate of point $Q$ is $-1$.

 

Calculate the distance of $RQ$ as follows:

 $$\begin{gathered} RQ=|-1-0| \\ =|-1| \\ =1 \end{gathered}$$

 

Thus, the distance of $RQ$ is 1 unit.

Part c. Step 1. Check the number line.

Consider the number line.

Part c. Step 2. Apply the concept.

On a number line, the coordinate of a point is the value that the point represents. 

 

The ruler postulate states that distance between two points equals the absolute value of the difference between their coordinates.

Part c. Step 3. Step description.

From the number line, the coordinate of point $P$ is $-2$ and the coordinate of point $T$ is $2$.

Calculate the distance of $RQ$ as follows:

$$\begin{gathered} PT=|-2-2| \\ =|-4| \\ =4 \end{gathered}$$

 

Thus, the distance of $PT$ is 4 unit.