# Location of a Point

The teacher plotted dot on a paper and asked the students to describe its location. Student x said that the dot is in the upper quarter of the paper, student y said that the dot is in the left end of the paper and student A said that the dot lies in the middle of the paper. So there were several responses.

Coordinates :

Locate the seat in your class. For this you need to know two numbers. That is the row number and the column number. For example (3, 2) which is 3 units from left edge and 2 units from bottom edge is plotted on a graph sheet. In a graph sheet we draw x and y axes conveniently and then fix the required point. 3 - is called x - coordinate of the point. 2 is the y-coordinate of the point. We say that the coordinates of the point are (3, 2). Always the first number indicates x - coordinate and the second number indicates y-coordinate.

Example

Plot the point (4, 5) on a graph sheet. Is it same as the point (5, 4)?

Solution

Locate x, y axes. Start at O(0,0). Move 4 units to the right, then move 5 units up we reach the point (4, 5). From the graph the points (4, 5) and (5, 4) are different points.

Example :

From the adjacent graph choose the letters that indicate the location of the points given        below.

(i) (5, 2)

(ii) (0, 1)

(iii) (6, 3)

(iv) coordinates of B

(v) coordinates of E

Solution:

(i) (5, 2) is the point A

(ii) (0, 1) is the point C.

(iii) (6, 3) is the point D.

(iv) Point B is (3, 4)

(v) Point E is (4, 6)

Example: Plot the following points and verify if they lie on a line. If they lie on a line name it.

(i) (0, 2) (0, 4) (0, 8.5), (0, 10)

(ii) A(2, 1), B(2, 3) C(2, 5), D(2, 7)

(iii) (1, 5) (2, 5) (3, 5) (4, 5)

(iv) (1, 4) (4, 1) (3, 2) (2, 3)

(i)

These lie on a line. The line is y axis.

(ii)

These lie on a line. The line is AD and parallel to y-axis

(iii)

These points lie on a line. The line is EH parallel to x -axis

(iv)

These lie on a line AD.

Linear Graph : A graph obtained by joining the plotted points in a line. Such graphs are called linear graph.