# If the perpendicular distance of a point P from the x-axis is 5 units and the foot ofthe perpendicular lies on the negative direction of x-axis, then the point P has  (A) x coordinate = $- 5 %u200B$ ​​​ (B) y coordinate = 5 only   (C) y coordinate = $- 5 %u200B$ only (D) y coordinate = 5 or $- 5 %u200B$

Answer: (D) y coordinate = 5 or -5

Solution.

We know that the perpendicular distance of any point from the x-axis gives y-coordinate of that point.
i.e.,  x coordinate is always perpendicular to y-axis.

(A) Here x-coordinate is -5. It lies on negative direction of x-axis so it is incorrect
(B) Here y-coordinate is 5. It lies on positive direction of y-axis and is perpendicular to x-axis so it is incorrect
(C) Here y-coordinate is -5. It lies on negative direction of y-axis and is perpendicular to x-axis.
So it is incorrect
(D) Here y-coordinate is 5 or -5, i.e., perpendicular distance can be in II quadrant or III quadrant. So that we can say the point P has y-coordinate 5 or -5
Therefore option (D) is correct

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