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Question
The points (other than origin) for which abscissa is equal to the ordinate will lie in
(a) I quadrant only
(b) I and II quadrants
(c) I and III quadrants
(d) II and IV quadrants
(a) I quadrant only
(b) I and II quadrants
(c) I and III quadrants
(d) II and IV quadrants
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Solution
In I quadrant: x > 0, y > 0
In II quadrant: x < 0, y > 0
In III quadrant: x < 0, y < 0
In IV quadrant: x > 0, y < 0
The points for which abscissa is equal to the ordinate, both x and y must be of same sign i.e. either x > 0, y > 0 or x < 0, y < 0.
The co-ordinates of the points for which abscissa is equal to the ordinate are of the form (x, y) or (−x, −y), where x = y.
Thus, the points (other than origin) for which abscissa is equal to the ordinate will lie in I and III quadrants.
Hence, the correct answer is option (c).
In I quadrant: x > 0, y > 0
In II quadrant: x < 0, y > 0
In III quadrant: x < 0, y < 0
In IV quadrant: x > 0, y < 0
The points for which abscissa is equal to the ordinate, both x and y must be of same sign i.e. either x > 0, y > 0 or x < 0, y < 0.
The co-ordinates of the points for which abscissa is equal to the ordinate are of the form (x, y) or (−x, −y), where x = y.
Thus, the points (other than origin) for which abscissa is equal to the ordinate will lie in I and III quadrants.
Hence, the correct answer is option (c).
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