Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 28 - Distance Formula [Latest edition]

Find the distance between the following pairs of points:

(–3, 6) and (2, –6)

Find the distance between the following pairs of points:

(a, b), (−a, −b)

Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`

Find the distance between the following pair of points:

`(sqrt(3)+1,1)` and `(0, sqrt(3))`

Find the distance between the origin and the point:
(-8, 6) 

Find the distance between the origin and the point:
(-5, -12)

Find the distance between the origin and the point:
(8, −15)

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

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

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

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

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

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

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

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

A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.

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

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.

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

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

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.

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

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

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

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.

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.

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: AT 

Point P (2, -7) is the centre of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of 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 y-axis whose distances from the 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.