Selina solutions concise maths class 9 icse Solutions for Chapter 28 chapter 28 distance formula

Exercises in Chapter 28 chapter 28 distance formula Grade 9

Exercise 28

Questions in Exercise 28

Find the distance between the following pairs of the point :

(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)

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

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

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

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.

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

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 units.

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

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

(i) AT

(ii) AB

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

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

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

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

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.

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.

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Chapters in this book

Chapter 1- Rational and Irrational Numbers

Chapter 2- Compound Interest [Without Using Formula

Chapter 3- Compound Interest [Using Formula

Chapter 4- Expansions

Chapter 5- Factorisation

Chapter 6- Simultaneous Equations

Chapter 7- Indices [exponents]

Chapter 8- Logarithms

Chapter 9- Triangles [Congruency in Triangles]

Chapter 10- Isosceles Triangle

Chapter 11- Inequalities

Chapter 12- Mid-Point and Its Converse

Chapter 13- Pythagoras Theorem

Chapter 14- Rectilinear Figures

Chapter 15- Construction of Polygons

Chapter 16- Area Theorems

Chapter 17- Circles

Chapter 18- Statistics

Chapter 19- Mean and Median

Chapter 20- Area and Perimeter of Plane Figures

Chapter 21- Solids

Chapter 22- Trigonometrical Ratios

Chapter 23- Trigonometrical Ratios of Standard Angles

Chapter 24- Solution Of Right Triangles

Chapter 25- Complementary angles

Chapter 26- Co-ordinate Geometry

Chapter 27- Graphical Solution

Chapter 28- Distance Formula