# Distance Formula Class-9 Concise Selina ICSE Maths Solutions

Distance Formula Class-9 Concise Selina ICSE Maths Solutions Chapter-28 . We provide step by step Solutions of Exercise / lesson-28 Distance Formula for ICSE Class-9 Concise Selina Mathematics by R. K. Bansal.

Our Solutions contain all type Questions with Exe-28 to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.

## Distance Formula Class-9 Concise Selina ICSE Maths Solutions Chapter-28

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Notes on Distance Formula,

Exe-28,

### Distance between two points

To calculate the distance between two points in a plane, we have to use distance formula as per described in coordinate geometry. With the help of this formula, we can find the distance between any two points marked in an x-y coordinate

### Distance Formula

Distance between two points P(x1,y1) and Q(x2,y2) is given by:

PQ = √[(x2– x1)2+ (y2– y1)2]

It is known as distance formula.

### Exe-28,Distance Formula Class-9 Concise Selina ICSE Maths Solutions

#### Questions. 1

Find the distance between the following pairs of points:

(i) (-3, 6) and (2, -6 )
(ii) (-a, -b) and (a, b)
(iii)(3/5 ,2) and (-1/5  , 1 ²/5)
(iv) (√3+1, 1) and (0, √3)

#### Questions. 2

Find the distance  between the origin and the point:

(i) (-8, 6)
(ii) (-5, -12)
(iii) (8, -15)

#### Questions. 3

The distance between the points (3, 1) and (0, x) is 5. Find x.

#### Questions. 4

Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).

#### Questions. 5

Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).

#### Questions. 6

A point A is at a distance of √10 unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.

#### Questions. 7

A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.

#### Questions. 8

What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?

#### Questions. 9

Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).

#### Questions. 10

A point P lies on the x-axis and another point Q lies on the y-axis.

(i) Write the ordinate of point P.
(ii) Write the abscissa of point Q.
(iii) If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.

#### Questions. 11

Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.

#### Questions. 12

Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS

#### Questions. 13

Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.

#### Questions. 14

Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.

#### Questions. 15

Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.

#### Questions. 16

Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if ‘a’ is negative and AB = CD.

#### Questions. 17

The vertices of a triangle are (5, 1), (11, 1) and (11, 9). Find the co-ordinates of the circumcentre of the triangle.

#### Questions. 18

Given A = (3, 1) and B = (0, y – 1). Find y if AB = 5.

#### Questions. 19

Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.

#### Questions. 20

The centre of a circle is (2x – 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.

#### Questions. 21

The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.

#### Questions. 22

Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of:

(i). AT

(ii). AB

#### Questions. 23

Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.

#### Questions. 24

Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.

#### Questions. 25

Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.

#### Questions. 26

Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.

#### Questions. 27

The distances of point P (x, y) from the points A (1, – 3) and B (- 2, 2) are in the ratio 2: 3.
Show that: 5x2 + 5y2 – 34x + 70y + 58 = 0.

#### Questions. 28

The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.