11+ Maths Solved Topic Wise Questions

1. What are coordinates?

Coordinates are a pair of numbers that help us find the position of points on a grid. Learning about coordinates and being able to plot points in graphs or maps is an essential skill for 11 plus exams.

1.1. Finding Coordinates of Points in graph

A graph has two axes: horizontal x-axis and a vertical y-axis. The point at which two axes intersect is called the origin - the coordinates of this point are (0, 0). Also along x-axis is positive x-axis and negative x-axis and along y-axis is positive and negative y-axes.

Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. The first number shows the position along the horizontal line or the x-axis. The second number shows the position along the vertical line or the y-axis.

Let's try to work out the coordinates of two points A and B labelled in the graph below.

• Coordinates of Point A :

  • Step 1 :

    • Position of point A on x-axis(horizontal) = 4
    • Position of point A on y-axis(vertical) = 2

  • Step 2 :

    • Position of point A in coordinate form:
    • Coordinates of A are (4,2)

• Coordinates of Point B :

  • Step 1:

    • Position of point B on x-axis(horizontal) = -2
    • Position of point B on y-axis(vertical) = -3

  • Step 2:

    • Position of point B in coordinate form:
    • Coordinates of B are (-2,-3)

2. How to plot coordinates?

a) Point (5,3)

• The first number in the brackets relates to the x axis.
• The 5 means moving five places to the right, along the x axis.
• The second number in the brackets relates to the y axis.
• The 3 means moving three places up, along the y axis.

b) Point (-3,2)

• The first number in the brackets relates to the x axis.
• The -3 means moving three places to the left, along the x axis.
• The second number in the brackets relates to the y axis.
• The 2 means moving two places down, along the y axis.

Let us now see the above two points on the graph,

2.1 Solved Example

a) Plot the points A(0,3), B(2,5), C(6,3) and D(2,1) on the above grid.

What is the name of the quadrilateral formed by line joining the points A,B,C and D?

b) What are the coordinates of point of intersection of the diagonals of quadrilateral ABCD?

Solution:

a) Plotting the points A, B, C and D using the method discussed above,

Quadrilateral ABCD is a Kite.

b) Diagonals are AC and BD.

E is the point of intersection of diagonals AC and BD.

Coordinates of E are (2,3)