Question

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 L=-5 ,M=0,N=8,P=-1,Q=7,R=4
seg MN and seg PQ
seg QR and seg LM
seg LP and seg NR
seg NP and seg LR​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

It is known that, distance between the two points is obtained by subtracting the smaller co-ordinate from larger co-ordinate.

(i) The co-ordinates of points B and E are 2 and 5 respectively. We know that 5 > 2.

∴ d(B, E) = 5 − 2 = 3

(ii) The co-ordinates of points J and A are −2 and 1 respectively. We know that 1 > −2.

∴ d(J, A) = 1 − (−2) = 1 + 2 = 3

(iii) The co-ordinates of points P and C are −4 and 3 respectively. We know that 3 > −4.

∴ d(P, C) = 3 − (−4) = 3 + 4 = 7

(iv) The co-ordinates of points J and H are −2 and −1 respectively. We know that −1 > −2.

∴ d(J, H) = −1 − (−2) = −1 + 2 = 1

(v) The co-ordinates of points K and O are −3 and 0 respectively. We know that 0 > −3.

∴ d(K, O) = 0 − (−3) = 0 + 3 = 3

(vi) The co-ordinates of points O and E are 0 and 5 respectively. We know that 5 > 0.

∴ d(O, E) = 5 − 0 = 5

(vii) The co-ordinates of points P and J are −4 and −2 respectively. We know that −2 > −4.

∴ d(P, J) = −2 − (−4) = −2 + 4 = 2

(viii) The co-ordinates of points Q and B are −5 and 2 respectively. We know that 2 > −5.

∴ d(Q, B) = 2 − (−5) = 2 + 5 = 7

Page No 5:

Question 2:

If the co-ordinate of A is x and that of B is y, find d(A, B) .

(i) x = 1, y = 7               (ii) x = 6, y = −2           (iii) x = −3, y = 7  

(iv) x = −4, y = −5        (v) x = −3, y = −6  (vi) x = 4, y = −8

ANSWER:

It is known that, distance between the two points is obtained by subtracting the smaller co-ordinate from larger co-ordinate.

(i) The coordinates of A and B are x and y respectively. We have, x = 1 and y = 7. We know that 7 > 1.

∴ d(A, B) = y − x = 7 − 1 = 6

(ii) The coordinates of A and B are x and y respectively. We have, x = 6 and y = −2. We know that 6 > −2.

∴ d(A, B) = x − y = 6 − (−2) = 6 + 2 = 8

(iii) The coordinates of A and B are x and y respectively. We have, x = −3 and y = 7. We know that 7 > −3.

∴ d(A, B) = y − x = 7 − (−3) = 7 + 3 = 10

(iv) The coordinates of A and B are x and y respectively. We have, x = −4 and y = −5. We know that −4 > −5.

∴ d(A, B) = x − y = −4 − (−5) = −4 + 5 = 1

(v) The coordinates of A and B are x and y respectively. We have, x = −3 and y = −6. We know that −3 > −6.

∴ d(A, B) = x − y = −3 − (−6) = −3 + 6 = 3

(vi) The coordinates of A and B are x and y respectively. We have, x = 4 and y = −8. We know that 4 > −8.

∴ d(A, B) = x − y = 4 − (−8) = 4 + 8 = 12

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