Distance between a point and a straight line

The distance from a point to a straight line on a plane is called the shortest distance from a point to a straight line in Euclidean geometry. The distance from a point to a straight line is equal to the length of the segment that connects the point to the straight line and is perpendicular to the straight line. The formula for calculating the distance from a point to a straight line on the plane: if the equation of the straight line is Ax + By + C = 0, then the distance from the point M(Mx, My) to the straight line can be found using the formula given below.

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The distance between a point and a straight line knowing the coordinates of the point and the equation of the straight line Enter the coordinates of the point:
М(;
)
and the equation of the straight line:
*x+
*y+
=0

Example of tasks for finding the distance from a point to a straight line on a plane

Example #1:  find the distance between the line 3x + 4y – 6 = 0 and the point M(-1, 4).
Answer: the distance from the point to the straight line is 1.4.

Example #2:  find the distance between the line 2x + 5y – 8 = 0 and the pointM(1, 14).
Answer: the distance from a point to a straight line is 11.88.