1. The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.
| Point | A | B | C | D | E |
|---|---|---|---|---|---|
| Co-ordinate | − 3 | 5 | 2 | − 7 | 9 |
- seg DE and seg AB
- seg BC and seg AD
- seg BE and seg AD
Solution:
The distance between two points on a number line is calculated by subtracting the smaller co-ordinate from the greater co-ordinate.
(i) seg DE and seg AB
D: − 7, E: 9, B: 5, C: 2
DE = 9 − (− 7)
∴ DE = 9 + 7)
∴ DE = 16
and
AB = 5 − (− 3)
∴ AB = 5 + 3
∴ AB = 8
Now, 16 ≠ 8
∴ seg DE and seg AB are not congruent.
(ii) seg BC and seg AD
B: 5, C: 2, A: − 3, D: − 7
BC = 5 − 2
∴ BC = 3
and
AD = − 3 − (− 7)
∴ AD = − 3 + 7
∴ AD = 4
Now, 3 ≠ 4
∴ seg BC and seg AD are not congruent.
(iii) seg BE and seg AD
B: 5, E: 9, A: − 3, D: − 7
BE = 9 − 5
∴ BE = 4
and
AD = − 3 − (− 7)
∴ AD = − 3 + 7
∴ AD = 4
Now, 4 = 4
∴ seg BE and seg AD are congruent.
2. Point M is the midpoint of seg AB. If AB = 8, then find the length of AM.
Solution:
M is the midpoint of seg AB. ... (Given)
∴ AM = \(\displaystyle \frac {1}{2}\) × AB
∴ AM = \(\displaystyle \frac {1}{2}\) × 8
∴ AM = 4
Therefore, the length of AM is 4.
3. Point P is the midpoint of seg CD. If CP = 2.5, find l (CD).
Solution:
P is the midpoint of seg CD. ... (Given)
∴ CD = 2 × CP
∴ CD = 2 × 2.5
∴ CD = 5
∴ l (CD) = 5.
4. If AB = 5 cm, BP = 2 cm and AP = 3.4 cm, compare the segments.
Solution:
2 < 3.4 < 5
∴ BP < AP < AB
5. Write the answers to the following questions with reference to figure 1.13:
(i) Write the name of the opposite ray of ray RP.
Ray RS or Ray RT
(ii) Write the intersection set of ray PQ and ray RP.
Ray PQ
(iii) Write the union set of ray PQ and ray QR.
Line RQ
(iv) State the rays of which seg QR is a subset.
Ray QR and Ray RQ etc.
(v) Write the pair of opposite rays with common end point origin R.
Ray RQ and Ray RT
(vi) Write any two rays with common end point origin S.
Ray SR and Ray ST
(vii) Write the intersection set of ray SP and ray ST.
Point S
6. Answer the questions with the help of figure 1.14.
(i) State the points which are equidistant from point B.
Point A and Point C
OR Point D and Point P
(ii) Write a pair of points equidistant from point Q.
Point U and Point L
OR Point R and Point P
(iii) Find d (U, V), d (P, C), d (V, B), d (U, L).
d (U, V)
Co-ordinate of U: − 5
Co-ordinate of V: 5
Now, − 5 < 5
∴ d (U, V) = 5 − (− 5)
∴ d (U, V) = 5 + 5
∴ d (U, V) = 10
d (P, C)
Co-ordinate of P: − 2
Co-ordinate of C: 4
Now, − 2 < 4
∴ d (P, C) = 4 − (− 2)
∴ d (P, C) = 4 + 2
∴ d (P, C) = 6
d (V, B)
Co-ordinate of V: 5
Co-ordinate of B: 2
Now, 5 > 2
∴ d (V, B) = 5 − 2
∴ d (V, B) = 3
d (U, L)
Co-ordinate of U: − 5
Co-ordinate of L: − 3
Now, − 5 < − 3
∴ d (U, L) = (− 3) − (− 5)
∴ d (U, L) = − 3 + 5
∴ d (U, L) = 2
This page was last modified on
15 April 2026 at 12:16