# 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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**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(x_{1},y_{1}) and Q(x_{2},y_{2}) is given by:

PQ = √[(x_{2}– x_{1})^{2}+ (y_{2}– y_{1})^{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)

**Answer 1:**

**Questions. 2 **

Find the distance between the origin and the point:

(i) (-8, 6)

(ii) (-5, -12)

(iii) (8, -15)

**Answer 2:**

**Questions. 3 **

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

**Answer 3:**

**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).

**Answer 4:**

**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).

**Answer 5:**

**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.

**Answer 6:**

**Questions. 7 **

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

**Answer 7:**

**Questions. 8 **

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

**Answer 8:**

**Questions. 9**

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

**Answer 9:**

**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.

**Answer 10:**

**Questions. 11**

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

**Answer 11:**

**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

**Answer 12:**

**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.

**Answer 13:**

**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.

**Answer 14:**

**Questions. 15**

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

**Answer 15:**

**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.

**Answer 16:**

**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.

**Answer 17:**

**Questions. 18**

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

**Answer 18:**

**Questions. 19**

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

**Answer 19:**

**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.

**Answer 20:**

**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.

**Answer 21:**

**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

**Answer 22:**

**Questions. 23**

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

**Answer 23:**

**Questions. 24**

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

**Answer 24:**

**Questions. 25**

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

**Answer 25:**

**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.

**Answer 26:**

**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: 5x^{2} + 5y^{2} – 34x + 70y + 58 = 0.

**Answer 27:**

**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.

**Answer 28:**

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