Question

Observe the number line (fig. 1.28) and answer the following questions.
(i) Write the co-ordinates of the points C, S, Q, D
(ii) Name the points whose co-ordinates are 4, 5, 0, -2
(iii) Find d(Q,T), d(E,B), d(O,C), d(O,R)
(iv) Name the points which are at a distance of 4 from point 0.

Answer 1

(i) The coordinates of the points are as follows:

$$\begin{gathered} \mathrm{C}=-3 \\ \mathrm{S}=4 \\ \mathrm{Q}=2 \\ \mathrm{D}=-4 \end{gathered}$$

(ii) The points whose coordinates are:

$$\begin{gathered} 4=\mathrm{S} \\ 5=\mathrm{T} \\ 0=\mathrm{O} \\ -2=\mathrm{B} \end{gathered}$$

(iii)

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{Q}=2 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{T}=5 \\ \mathrm{As}5>2,\mathrm{d}(\mathrm{Q},\mathrm{T})=5-2=3 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{E}=-5 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{B}=-2 \\ \mathrm{As}-2>-5,\mathrm{d}(\mathrm{Q},\mathrm{T})=-2-(-5)=3 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{O}=0 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{C}=-3 \\ As0>-3,\mathrm{d}(\mathrm{Q},\mathrm{T})=0-(-3)=3 \end{gathered}$$

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{O}=0 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{R}=3 \\ \mathrm{As}3>0,\mathrm{d}(\mathrm{Q},\mathrm{T})=3-0=3 \end{gathered}$$

(iv) The points which are at a distance of 4 from O are S and D.

$$\begin{gathered} \mathrm{Coordinate}\mathrm{of}\mathrm{O}=0 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{S}=4 \\ \mathrm{As}4>0,\mathrm{d}(\mathrm{S},\mathrm{O})=4-0=4 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{O}=0 \\ \mathrm{Coordinate}\mathrm{of}\mathrm{D}=-4 \\ \mathrm{As}0>-4,\mathrm{d}(\mathrm{D},\mathrm{O})=0-(-4)=4 \end{gathered}$$