Question

Answer the questions with the help of a given figure.

1. State the points which are equidistant from point B.
2. Write a pair of points equidistant from point Q.
3.  Find d(U, V), d(P, C), d(V, B), d(U, L).

Answer 1

(i) The co-ordinates of points B and C are 2 and 4 respectively.

We know that 4 > 2

∴ d(B, C) = 4 − 2

∴ d(B, C) = 2

The co-ordinates of points B and A are 2 and 0 respectively.

We know that 2 > 0

∴ d(B, A) = 2 − 0

∴ d(B, A) = 2

Since d(B, A) = d(B, C), then points A and C are equidistant from point B.

The co-ordinates of points B and D are 2 and 6 respectively.

We know that 6 > 2

∴ d(B, D) = 6 − 2

∴ d(B, D) = 4

The co-ordinates of points B and P are 2 and −2 respectively.

We know that 2 > − 2

∴ d(B, P) = 2 − (− 2)

∴ d(B, P) = 2 + 2

∴ d(B, P) = 4

Since d(B, D) = d(B, P), then points D and P are equidistant from point B.

(ii) The co-ordinates of points Q and U are −4 and −5 respectively.

We know that −4 > −5

∴ d(Q, U) = − 4 − (− 5)

∴ d(Q, U) = − 4 + 5

∴ d(Q, U) = 1

The co-ordinates of points Q and L are −4 and −3 respectively.

We know that − 3 > − 4

∴ d(Q, L) = −3 − (− 4)

∴ d(Q, L) = −3 + 4

∴ d(Q, L) = 1

Since d(Q, U) =  d(Q, L), then points U and L are equidistant from point Q.

The co-ordinates of points Q and R are −4 and −6 respectively.

We know that − 4 > − 6

∴ d(Q, R) = −4 − (−6)

∴ d(Q, R) = −4 + 6

∴ d(Q, R) = 2

The co-ordinates of points Q and P are −4 and −2 respectively.

We know that −2 > − 4

∴ d(Q, P) = −2 − (− 4)

∴ d(Q, P) = −2 + 4

∴ d(Q, P) = 2

Since d(Q, R) =  d(Q, P), then points R and P are equidistant from point Q.

(iii) The co-ordinates of points U and V are −5 and 5 respectively.

We know that 5 > − 5

∴ d(U, V) = 5 − (− 5)

∴ d(U, V) = 5 + 5

∴ d(U, V) = 10

The co-ordinates of points P and C are −2 and 4 respectively.

We know that 4 > −2

∴ d(P, C) = 4 − (− 2)

∴ d(P, C) = 4 + 2

∴ d(P, C) = 6

The co-ordinates of points V and B are 5 and 2 respectively.

We know that 5 > 2

∴ d(V, B) = 5 − 2

∴ d(V, B) = 3

The co-ordinates of points U and L are −5 and −3 respectively.

We know that − 3 > − 5

∴ d(U, L) = −3 − (−5)

∴ d(U, L) = −3 + 5

∴ d(U, L) = 2