Question

Select the correct alternative from the answers of the questions given below.

(i) How many mid points does a segment have ?

(A) only one (B) two (C) three (D) many

(ii) How many points are there in the intersection of two distinct lines ?

(A) infinite (B) two (C) one (D) not a single

(iii) How many lines are determined by three distinct points ?

(A) two (B) three (C) one or three (D) six

(iv) Find d(A, B), if co-ordinates of A and B are $-$ 2 and 5 respectively.

(A)$-$2 (B) 5 (C) 7 (D) 3

(v) If P - Q - R and d(P,Q) = 2, d(P,R) = 10, then find d(Q,R).
(A) 12 (B) 8 (C) $\sqrt{96}$ (D) 20

Answer 1

(i) Every segment has one and only one midpoint.
Hence, the correct answer is option (A).

(ii) It is known that, two distinct lines intersect at one point.
Hence, the correct answer is option (C).

(iii) Consider the 3 distinct points as P, Q and R.
Suppose the points P, Q and R are collinear.

So, only one line is determined by the points P, Q and R.
Suppose the points P,Q and R are non collinear.

So, three lines can be determined by the points P, Q and R.
Hence, the correct answer is option(C).

(iv) The co-ordinates of points A and B are $-$2 and 5 respectively. We know that 5 > ​$-$2.
∴ d(A, B) = 5 − (−2) = 5 + 2 = 7
Hence, the correct answer is option(C).

(v) It is given that, point Q is between point P and point R.

We have, d(P,Q) = 2; d(P,R) = 10
Now, d(P,R) = d(P,Q) + d(Q,R)
∴ d(Q,R) = d(P,R) − d(P,Q) = 10 − 2 = 8
Hence, the correct answer is option (B).