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(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)
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: 5x2 + 5y2 – 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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