Decide which of the following statements is true and which is false. Give reasons for your answer.

Question:

Decide which of the following statements is true and which is false. Give reasons for your answer.

(i)  A point whose x-coordinate is zero, will lie on the y-axis.

(ii) A point whose y-coordinate is zero, will lie on x-axis.

(iii) The coordinates of the origin are (0, 0).

(iv) Points whose x and y coordinates are equal, lie on a line passing through the origin.

Solution:

(i) The examples of points having x-coordinate as zero are (0,3), (0,6), (0,9). This can be represented in the following manner:

From the figure, it can be seen that these points lie on the y-axis. Hence, the statement is true.

(ii) The examples of points having y-coordinate as zero are (3,0), (6,0), (9,0). This can be represented in the following manner:

From figure above, it can be seen that these points lie on the x-axis. Hence, the statement is true.

(iii) The origin divides each of these axes into a positive and a negative semi-axis. The coordinates of the origin are always are zero, i.e. (0,0). Thus, the statement is true.

(iv) The examples of points having equal x and y coordinates are (0,0), (1,1), (2,2), etc. If these points are joined, they will lie on a line passing through the coordinates (0,0). Thus, the statement is true.