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mathematics UK Year 9 Mathematics (KS3)
 
Solved problems for the chapter:
 

Cartesian Plane

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:cartesian_plane/4312/


Example 1.

Plot the points , , , ) and in the coordinate system.

    
Example 2.

Draw pairs of points in the coordinate system and connect each pair of points with a line.


A (0, 2) and B (-4, -2)

C (1, 1) and D (2, 3)

E (1, 2) and F (0, 3)

    
3.
Determine the set of points by their position.

A (3, 3), B (3, -3)

    
4.
Determine the set of points by their position.

N (0, 4), O (0, -2)

    
5.
Determine the set of points by their position.

C (2, -4), D (-2, -4)

    
6.
Determine the set of points by their position.

P (-2, -4), Q (-2, 1), R (-2, 3)

    
7.
Determine the set of points by their position.

E (3, 3), F (0, 0), G (-4, -4)

    
8.
Determine the set of points by their position.

S (-4, 3), T (5, 3), U (-1, 3)

    

9.
Determine the set of points by their position.

H (-3, 3), I (-4, 4), J (2, -2)

    
10.
Determine the set of points by their position.

V (-2, 3), Z (2, -3)

    
11.
Determine the set of points by their position.

K (4, 0), L (2, 0), M (-3, 0)

    
12.
In a rectangular coordinate system, draw a set of points (x, y) for which:

x = 2

    
13.

Plot the given points in the coordinate system, then mirror them across the abscissa axis and write down the new coordinates of the points.


A(3, 4), B(-1, 3), C(0, 2) and D(-3,-2)

    
14.

Plot the given points in the coordinate system, then mirror them across the ordinate axis and write down the new coordinates of the points.


A(3, 4), B(-1, 3), C(-2, 0) and D(-1, -3)

    
15.

The points A(1, 1), B(3, 5) and C lie on the same line. The point A lies between points B and C and equidistant from both. Obtain the coordinates of the point C.

    
16.

A set of points in the coordinate system is drawn. Obtain the inequality represented.


    
17.

A set of points in the coordinate system is drawn. Write an inequality to describe this.


    
18.
In a rectangular coordinate system, draw a set of points (x, y) for which:

y = 3

    

19.

A set of points in the coordinate system is drawn. Obtain the inequality represented by this.


    
20.

In the coordinate system, plot the set of points T(x, y), which corresponds to the conditions and . Shade the resulting figure and calculate its area.

    
21.
In a rectangular coordinate system, draw a set of points (x, y) for which:

x = -3

    
22.
In a rectangular coordinate system, draw a set of points (x, y) for which:

y = -1

    
23.
In a rectangular coordinate system, draw a set of points (x, y) for which:

x = 0

    
24.
In a rectangular coordinate system, draw a set of points (x, y) for which:

y = 0

    
25.
In a rectangular coordinate system, draw a set of points (x, y) for which:

y = x

    
26.
In a rectangular coordinate system, draw a set of points (x, y) for which:

y = -x

    
27.
In a rectangular coordinate system, draw a set of points (x, y) for which:

x < 0

    
28.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    

29.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
30.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
31.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
32.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
33.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
34.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
35.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
36.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
37.
In a rectangular coordinate system, draw a set of points (x, y) for which:

.

    
38.
In a rectangular coordinate system, draw a set of points (x, y) for which:

.

    

39.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
40.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
41.
In a rectangular coordinate system, draw a set of points (x, y) for which:

In the coordinate system, plot the set of all points for which applies.

    
42.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
43.
In a rectangular coordinate system, draw a set of points (x, y) for which:

    
44.
In a rectangular coordinate system, draw a set of points (x, y) for which: