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Question

# Answer the questions with the help of a given figure. (i) State the points which are equidistant from point B. (ii) Write a pair of points equidistant from point Q. (iii) Find d(U,V), d(P,C), d(V,B),d(U, L).

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Solution

## (i) The co-ordinates of points B and C are 2 and 4 respectively. We know that 4 > 2. ∴ d(B, C) = 4 − 2 = 2 The co-ordinates of points B and A are 2 and 0 respectively. We know that 2 > 0. ∴ d(B, A) = 2 − 0 = 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 = 4 The co-ordinates of points B and P are 2 and −2 respectively. We know that 2 > −2. ∴ d(B, P) = 2 − (−2) = 2 + 2 = 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) = −4 + 5 = 1 The co-ordinates of points Q and L are −4 and −3 respectively. We know that −3 > −4. ∴ d(Q, L) = −3 − (−4) = −3 + 4 = 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) = −4 + 6 = 2 The co-ordinates of points Q and P are −4 and −2 respectively. We know that −2 > −4. ∴ d(Q, P) = −2 − (−4) = −2 + 4 = 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) = 5 + 5 = 10 The co-ordinates of points P and C are −2 and 4 respectively. We know that 4 > −2. ∴ d(P, C) = 4 − (−2) = 4 + 2 = 6 The co-ordinates of points V and B are 5 and 2 respectively. We know that 5 > 2. ∴ d(V, B) = 5 − 2 = 3 The co-ordinates of points U and L are −5 and −3 respectively. We know that −3 > −5. ∴ d(U, L) = −3 − (−5) = −3 + 5 = 2

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