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# Distance Between Two Points (given Their Coordinates)

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;
Where ‘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 points.
Or in other words the length of the line segment is also said to be the distance of a line.
Or the distance from a Point to a line when the coordinates are: (p1, q1) and (p2, q2);
Then the distance between two points given their coordinates 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 is ‘p’ and ‘q’ is given by:
D = |p – q| = √∑a = 1|pa – qa|2,
Suppose we have the coordinates 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:
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.

## Vertical and Horizontal Lines

Slope of line is basically the measure of Inclination of a Line. Here we will discuss about vertical and horizontal lines. In a coordinate plane there are two axes known as x and y -axis, these axes are represented by horizontal and vertical lines respectively. When x - coordinate is constant and y –coordinate changes then line is called as vertical line. A...Read More