Question

If the ordinate of a point is equal to its abscissa; then justify the statement that the point lies either in the first quadrant or in the second quadrant.

Answer 1

Hint: In order to solve this problem you have to construct the coordinates and then observe the point where abscissa and ordinate are equal. Doing this will solve your problem.

Complete step-by-step answer:

Abscissa and ordinate is equal means the x and y coordinates are the same in value and sign.
We can clearly see from the figure above that in the first and fourth quadrant both x and y coordinates are of the same sign so it is the only possible condition where x and y can have the same value.

Hence, the given statement is wrong that in the second quadrant abscissa and ordinate is equal. But it is true that in the first quadrant both the values can be the same.

Note: In this problem we need to just know that the ordinate is the point on the y-axis and the abscissa is the point on x-axis. By drawing the axes you can visualize the answer from that figure. Doing like this you will get the right answer.