Perpendicularity and Distance of a Point from a Line

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.

What are the values of x and y, if (x + 1, 4) = (5, y – 1)?

1. x = 5, y = 4

2. x = 4, y = 5

3. x = 5, y = 5

4. x = 4, y = 4

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.

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. 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)

Q. The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is
(a)

(b)

(c)

(d)

Q.

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

1. -2

2. -3

3. -1

4. 0

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. 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]