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# Distance From A Point To A Line

The Distance between two points is given by
D = √ (dp2 + dq2);
Where ‘D’ is the distance;
‘P’ is the coordinates of x – axis;
‘Q’ is the coordinates of y – axis;
‘dp’ is the difference between the x – coordinates of the points;
And ‘dq’ is the difference between the y – coordinates of the points.
Suppose we have coordinates of the points then we use the above formula for finding the distance between the coordinates of the Point.
Or in other words the length of the line segment is also said to be the distance of a line.
The Distance From a Point to a Line when the coordinates are: (p1, q1) and (p2, q2);
Then the distance between two points is given by the pythagoras theorem:
D = √ (p2 - p1)2 + (q2 - q1)2;
And the formula for three coordinates (p1, q1, r1) and (p2, q2, r2) then the distance between three points is given by:
D = √ (p2 - p1)2 + (q2 - q1)2+ (r2 - r1)2;
And in general the distance between two points ‘p’ and ‘q’ is given by:
D = |p – q| = √∑a = 1|pa – qa|2,
Suppose we have the coordinates of a points are (5, 8) and (-9, -3) then find the distance between two points.
We know that the coordinates of the points is (p1, q1) and (p2, q2);
Here the value of p1 = 5;
And the value of p2 = -9;
The value of q1 = 8;
The value of q2 = -3;
Then the distance between two points is:
The formula for finding the distance between two points is:
D = √ (p2 - p1)2 + (q2 - q1)2;
Then put the values in the given formula:
D = √ ((-9) - 5)2 + ((-3) - 8)2;
On further solving we get:
D = √ (14)2 + (-11)2;
D = √ 196 + 121;
D = √317;
D = 17.80.
So the distance from point to line is 17.80.

## Using Trigonometry

There are several problems in mathematics that involve use of Trigonometry for finding the quantities like height of a tower or a pole or any other vertical distance, angle of elevation and demotion, horizontal distances etc. Trigonometry can be categorized in following:
1.      Core
2.      Plane
3.      Spherical
4.      Analytic

Let us now understand how to so...Read More

## Using Two Line Equations

Line is a straight figure having one dimesion. Representation of linear relationships between the variables is shown by drawing a line. Using two line equations we can find out whether two lines are parallel to each other or not. If two lines are lying in a plane such that we get an Intersection Point on solving them (i.e. the values of unknown variables are pos...Read More

## When the Line is Horizontal and Vertical

Vertical line can be defined as the line whose x- coordinate remains same and y –coordinate changes. We can say a line which goes straight up and down and also parallel to the y – axis of the coordinate plane is known as vertical line. All points lie on the line having same x – coordinate. No Slope is defined for vertical line.