Betweenness

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?

1. None of the above
2. Point A is between point B and point C.
3. Point B is between point A and point C.
4. 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?

1. Point Q lies between P and R

2. Point P lies between Q and R

3. Point R lies between Q and P

4. 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?

1. Point Q is between P and R.
2. Point R is between P and Q.
3. Point P is between R and Q.
4. None of the above.

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

1. d(A, B) = 45, d(B, C) = 22, d(A, C) = 23.
2. d(A, B) = 36, d(B, C) = 90, d(A, C) = 64.
3. d(A, B) = 10, d(B, C) = 10, d(A, C) = 20.
4. 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.

1. 10
2. 20
3. 30
4. 5

Q.

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

1. $y=3or9$
2. $y=3or-9$
3. $y=-3or-9$
4. $y=-3or9$

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.

1. 2
2. 8
3. 10
4. 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?

1. None of the above
2. Point U is between the points V and A.
3. Point V is between the points U and A.
4. 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

1. 30
2. 70
3. 50
4. 20

Q.

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

1. 20

2. 2

3. 10

4. 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?

1. Point A is between point B and Point C.
2. Point C is between point A and Point B.
3. None of the above
4. 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) = ________.

1. 10
2. 12
3. 30
4. 32

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

1. 12
2. 8
3. 20
4. 2

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

1. 30
2. 40
3. 70
4. 10

Q.

The value of cos60 is

1. 1/2

2. 3/4

3. root(3)/4

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

1. 6

2. 7

3. 6.5

4. 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?

1. True

2. 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