Question

The co-ordinates of the points on the number line are as follows.

Points	P	Q	R	S	T
Co-ordinates	-3	5	2	-7	9

Find the lengths of : seg PQ, seg PR, seg PS, seg PT, seg QR, seg QS, seg QT, seg RS, seg RT, seg ST.

Answer 1

Given:
Coordinates of P = $-$3
Coordinates of Q = 5
Coordinates of R = 2
Coordinates of S = $-$ 7
Coordinates of T = 9

Now, we have the following:

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{Q}>\mathrm{coordinate}\mathrm{of}\mathrm{P} \\ \therefore \mathrm{seg}\mathrm{PQ}=5-(-3)=8 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{R}>\mathrm{coordinate}\mathrm{of}\mathrm{P} \\ \therefore \mathrm{seg}\mathrm{PR}=2-(-3)=5 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{P}>\mathrm{coordinate}\mathrm{of}\mathrm{S} \\ \therefore \mathrm{seg}\mathrm{PS}=-3-(-7)=4 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{T}>\mathrm{coordinate}\mathrm{of}\mathrm{P} \\ \therefore \mathrm{seg}\mathrm{PT}=9-(-3)=12 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{Q}>\mathrm{coordinate}\mathrm{of}\mathrm{R} \\ \therefore \mathrm{seg}\mathrm{QR}=5-2=3 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{Q}>\mathrm{coordinate}\mathrm{of}\mathrm{S} \\ \therefore \mathrm{seg}\mathrm{QS}=5-(-7)=12 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{T}>\mathrm{coordinate}\mathrm{of}\mathrm{Q} \\ \therefore \mathrm{seg}\mathrm{QT}=9-5=4 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{R}>\mathrm{coordinate}\mathrm{of}\mathrm{S} \\ \therefore \mathrm{seg}\mathrm{RS}=2-(-7)=9 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{T}>\mathrm{coordinate}\mathrm{of}\mathrm{R} \\ \therefore \mathrm{seg}\mathrm{RT}=9-2=7 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{T}>\mathrm{coordinate}\mathrm{of}\mathrm{S} \\ \therefore \mathrm{seg}\mathrm{PQ}=9-(-7)=16 \end{gathered}$$