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.

Answer 1

(i)For x = 0, we have x- coordinates as zero.

For example (0,5) and (0, 7)

These points will lie on y axis. Hence, we say that our given statement is true.

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

For y = 0, we have y- coordinates as zero.

For example (5,0) and (7, 0)

These points will lie on x axis. Hence, we say that our given statement is true.

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

Origin is intersection of x-axis and y-axis. This means that coordinates of the origin will be intersection of lines y = 0 and x = 0.

Hence, coordinates of origin are (0,0).

∴ Given statement is true.

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

For above statement we can conclude that our statement satisfies the equation x = y.

For x = 0 and y = 0, this equation gets satisfied.

Hence, our given statement is true.