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7

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.

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.