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Question
How many lines can be drawn which are perpendicular to a given line and pass through a given point lying (i) outside it? (ii) on it?
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Solution
(i) Explanation:
Perpendicular line from a given point to a given line is the shortest distance between them.
Only one shortest distance is possible. Thus, only one perpendicular line is possible from the given point (outside the line) to a given line.
(ii) Explanation:
At any point on the line, we can draw only one perpendicular line.
Thus, on the given line on a point, we can draw only one perpendicular line.
Perpendicular line from a given point to a given line is the shortest distance between them.
Only one shortest distance is possible. Thus, only one perpendicular line is possible from the given point (outside the line) to a given line.
(ii) Explanation:
At any point on the line, we can draw only one perpendicular line.
Thus, on the given line on a point, we can draw only one perpendicular line.
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