Perpendicularity and Distance of a Point from a Line

Q. Given ∠A and ∠B are supplementary angles, prove that
∠B < 180°. Furthermore, if ratio of A : B is 1 : 2, find the value of ∠B.
[ 3 Marks]

Q.

Two points P & Q are marked on the number line as shown in the figure. The co-ordinate of Q is 9 and the distance between them is 17 units. The co-ordinate of P is

1. 8

2. 9

3. -9

4. -8

Q. The distance between any two points is a ___________.

1. negative real number
2. non-negative real number
3. None of the above
4. complex number

Q. If the coordinates of points A and B on a number line are -2 and 5 respectively, then the distance d(A, B) is __________.

1. -2
2. 5
3. 3
4. 7

Q. If the coordinates of A and B are -3 and -6 respectively, then the distance d(A, B) is __________.

1. -3
2. 6
3. -6
4. 3

Q.

The distance between two points $\frac{-1}{2}$ and $\frac{2}{3}$ on the number line is

1. $3\frac{1}{2}$ units

2. $2\frac{1}{3}$ units

3. $2\frac{1}{6}$ units

4. $1\frac{1}{6}$ units

Q.

The distance between the points $4\frac{1}{2}$ and $3\frac{1}{4}$ on the number line is

1. $1\frac{1}{4}$ units

2. $2\frac{1}{4}$ units

3. $1\frac{1}{2}$ units

4. $2\frac{1}{3}$ units

Q.

The midpoint of the points 1 and -5 on the number line is

1. -2

2. -3

3. -1

4. 0

Q. Coordinates of A, B, C, D, E are 0, 2, 5, 4, -1 respectively. Sort the following in increasing order from top.

1. d(A, D)
2. d(A, C)
3. d(B, C)
4. d(E, A)