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Show that of all line sents drawn from a given point not on it, the perpendicular line sent is the shortest.

Show that of all line sents drawn from a given point not on it, the perpendicular line sent is the shortest.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
. AP is perpendicular line segment on line l and AQ is any other line segment. A L APQ > L AQP [In a triangle, if an angle is 90°, other two angles are less than 90°.] < P a > / => AQ > AP. Hence, any line segment AQ, from point A to the line l, is greater than the perpendicular line segment AP, from point A to the line l. Hence, AP is the shortest segment of all the segments.

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