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

Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes.
x - 2y - 4 = 0
2x + y = 3

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically : 
(i) the area of a triangle;
(ii) the coordinates of the vertices of the triangle.

The cost of manufacturing x articles is Rs. (50 + 3x). The selling price of x articles is Rs. 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.

Use your graph to determine:
No. of articles to be manufactured and sold to break even (no profit and no loss).

The cost of manufacturing x articles is Rs.(50 + 3x). The selling price of x articles is Rs. 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.

Use your graph to determine:
The profit or loss made when (a) 30 (b) 60 articles are manufactured and sold.

Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively. Take 1 cm = 1 unit on both the axes.

Using the same axes of co-ordinates and the same unit, solve graphically :
x + y = 0 and 3x - 2y = 10.
(Take at least 3 points for each line drawn).

Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.

Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`

The course of an enemy submarine, as plotted on rectangular co-ordinate axes, gives the equation 2x + 3y = 4. On the same axes, a destroyer's course is indicated by the graph x - y = 7. Use the graphical method to find the point at which the paths of the submarine and the destroyer intersect?

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.