Shortest distance of a point from a line

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Shortest distance of a point from a line
Let us consider a point and a line as shown in the below figure.

We can find many distances from a line to a point by drawing different line segments as shown in the below figure.

Let us draw a circle with the above considered point as centre and distance of the point from line along the perpendicular line segment to the considered line as radius.
It will be like the below figure.

We know that the points on the circle will be at same distance from centre.
If we observe the above figure, the distance of the point from considered line along line segments other than the perpendicular line segment to the considered line will be greater than the radius of the drawn circle.

Therefore, the distances of the point from line along line segments other than the perpendicular line segment to the considered line will be greater than the distance of the point along the perpendicular line segment to the considered line as the distance of the point from line along the perpendicular line segment to the considered line is equal to the radius of drawn circle.

Therefore, the distance of the point from the line along the perpendicular line segment to the line is the shortest distance of the point from the line.

Therefore, the shortest distance of a point from a line will be equal to the distance of the point from line along the perpendicular line to the considered line.


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