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