Question

Which of the following statements is false?
(a) The x-coordinates of all the points to the right side of the y-axis are positive.
(b) The y-coordinates of all the points above the x-axis are positive.
(c) The y-coordinates of all the points below the x-axis are positive.
(d) The x-coordinates of all the points to the left side of the y-axis are negative.

Answer 1

Hint: We start solving the problem by drawing the figure representing x and y-axes. We then check the sides to the y-axis where the positive and negative values for x-coordinates are found. We then check the sides to the x-axis where the positive and negative values for y-coordinates are found to get the required answer.

Complete step by step answer:
According to the problem, we are asked to state which of the given options are false.
Let us draw the figure representing the x-axis and y-axis.

From the figure, we can see that the positive values of x lie on the right side of the y-axis. So, option (a) is true.
From the figure, we can see that the negative values of x lie on the left side of the y-axis. So, option (d) is true.
From the figure, we can see that the positive values of y lie above the x-axis. So, option (b) is true.
From the figure, we can see that the negative values of y lie below the x-axis. So, option (c) is false.
$\therefore $ The correct option for the given problem is (c).
Note:
 We should know that the points with positive x-coordinates lie on the side where the values on the x-axis are positive. Similarly, the points with negative x-coordinates, positive y-coordinates, negative y-coordinates lie on the side where the values on the x-axis are negative and the values on the y-axis are positive, negative. Similarly, we can expect problems to find the angle between x and y-axes.