# Betweenness

## Trending Questions

**Q.**On a number line, points A, B and C are such that d(A, B) = 5 units, d(B, C) = 11 units and d(A, C) = 6 units. Which of the points is between the other two?

- None of the above
- Point A is between point B and point C.
- Point B is between point A and point C.
- Point C is between point A and point B.

**Q.**

P, Q, and R are 3 points on a straight line. QP = 5 cm, PR = 10 cm and QR = 15 cm.

Which of the following is true?

Point Q lies between P and R

Point P lies between Q and R

Point R lies between Q and P

Point P lies exactly in the middle of QR.

**Q.**47. The incentre of the triangle formed by (1, 2), (3, 4) and (2, 3) is 1) does not exist 2)(-2, 3) 3)(2, -3) 4)(3, 3)

**Q.**

A(2, 2) , B(-2, -2), C(-2√3, 2√3) . Show that the following points take in order form an equilateral triangle ?

**Q.**The distance of the point P (4, 3) from the origin is

(a) 4

(b) 3

(c) 5

(d) 7

**Q.**On a number line, points A, B and C are such that d(A, C) = 10, d(C, B) = 8 . Find d(A, B) considering all possibilities.

**Q.**If P, Q, R are three distinct collinear points, then which of the following is/are possible?

- Point Q is between P and R.
- Point R is between P and Q.
- Point P is between R and Q.
- None of the above.

**Q.**Choose the correct option from the following which states that point A is between point B and point C.

- d(A, B) = 45, d(B, C) = 22, d(A, C) = 23.
- d(A, B) = 36, d(B, C) = 90, d(A, C) = 64.
- d(A, B) = 10, d(B, C) = 10, d(A, C) = 20.
- d(A, B) = 17, d(B, C) = 23, d(A, C) = 40.

**Q.**If P - Q - R and d(P, Q) = 10 units, d(P, R) = 20 units, then d(Q, R) = ________ units.

- 10
- 20
- 30
- 5

**Q.**

On a number line, co-ordinates of P, Q, R are 3, $-$ 5 and 6 respectively. State with reason whether the following statements are true or false.

(i) d(P, Q) + d(Q, R) = d(P, R)

(ii) d(P, R) + d(R, Q) = d(P, Q)

(iii) d(R, P) + d(P, Q) = d(R, Q)

(iv) d(P, Q) $-$ d(P, R) = d(Q, R)

**Q.**Find the values of y for which the distance between the points P (2, - 3) and Q (10, y) is 10 units

- y=3 or 9
- y=3 or −9
- y=−3 or −9
- y=−3 or 9

**Q.**If d(Q, R) = 25, d(P, R) = 45, what should be the value of d(P, Q) if the points P, Q, and R are on the same straight line and Q lies in between P and R?

**Q.**If AB = 8 units and M is the midpoint of AB, then AM = ________ units.

- 2
- 8
- 10
- 4

**Q.**On a number line, points U, V and A are such that d(U, A) = 215 units, d(V, A) = 140 units and d(U, V) = 75 units. Which of the points is between the other two?

- None of the above
- Point U is between the points V and A.
- Point V is between the points U and A.
- Point A is between the points U and V.

**Q.**If P, Q, R are three distinct collinear points, then which of the following is/are possible?

1. Point Q is between P and R.

2. Point R is between P and Q.

3. Point P is between R and Q.

**Q.**If d(Q, R) = 25, d(P, R) = 45, What must be the value of d(P, Q) if the points P, Q, R are on the same straight line and Q lies in between P and R

- 30
- 70
- 50
- 20

**Q.**

What is the distance of the point (-6, 8) from the origin?

20

2

10

14

**Q.**On a number line, points A, B and C are such that d(A, B) = 81, d(B, C) = 54 and d(A, C) = 36. Which of the points is between the other two?

- Point A is between point B and Point C.
- Point C is between point A and Point B.
- None of the above
- Point B is between point A and Point C.

**Q.**If A - B - C and d(B, C) = 11, d(A, B) = 21, then d(A, C) = ________.

- 10
- 12
- 30
- 32

**Q.**If P - Q - R and d(P, Q) = 2 units, d(P, R) = 10 units, then d(Q, R) = ________ units.

- 12
- 8
- 20
- 2

**Q.**If P - Q - R and d(Q, R) = 30 units, d(P, R) = 70 units, then d(P, Q) = ________ units.

- 30
- 40
- 70
- 10

**Q.**

The value of cos60 is

1/2

3/4

root(3)/4

root(3)/4

**Q.**On a number line, points A, B and C are such that d(A, C) = 10, d(C, B) = 8. Find d(A, B) considering all possibilities.

**Q.**

The midpoint of 5 and 8 is

6

7

6.5

any number between 6 and 7

**Q.**Find the co-ordinates of the point A which divides segment GH internally in the ratio m:n

(i) G $\cong $ (5, 8), H $\equiv $($-$7, $-$8), m:n = 4:1

(ii) G $\equiv $ ($-$4, 12), H $\equiv $ (11, $-$3), m:n = 2:3

**Q.**On a number line, points A, B, and C are such that d(A, B) = 5 units, d(B, C) = 11 units, and d(A, C) = 6 units. Which of the points is between the other two?

**Q.**On a number line, points A, B and C are such that d(A, B) = 81, d(B, C) = 54 and d(A, C) = 36. Which of the points is between the other two?

**Q.**

Puppy says that P (5, 6) is same as point Q (6, 5). Is he correct?

True

False

**Q.**On a number line, points U, V and A are such that d(U, A) = 215 units, d(V, A) = 140 units and d(U, V) = 75 units. Which of the points is between the other two?

[2 Marks]

**Q.**In each of the following, decide whether the relation of betweenness exists among the points A, B and D. Name the point which lies between the other two.

(i) d(A, B) = 5, d(B, D) = 8, d(A, D) = 11

(ii) d(A, B) = 11, d(B, D) = 6, d(A, D) = 5

(iii) d(A, B) = 2, d(B, D) 15, d(A, D) = 17