Mathematics

# Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

##### SOLUTION

(Refer to Image)
Take a point P not on AB straight line, but some distance away from AB. We draw PC (the perpendicular on to AB). We draw another line from P to D.
In the triangle PCD, use the Pythagorean law for sides:
$PC^2+CD^2=DP^2$
Since $CD^2$ is positive and adds to $PC^2$
$\therefore PC^2+CD^2 >PC^2$
or, $DP^2 >PC^2$
So, $DP >PC$
So, $PC$ the perpendicular distance from an external point to a line segment, is the shortest.

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

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