(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Find the distance between the following pairs of points:

(–3, 6) and (2, –6)

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.