Question

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 1

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