Input Data :
Point 1`(x_A, y_A)` = (4, 3)
Point 2`(x_B, y_B)` = (3, -2)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points = `\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}`
Solution :
Distance between two points = `\sqrt((3 - 4)^2 + (-2 - 3)^2)`
= `\sqrt((-1)^2 + (-5)^2)`
= `\sqrt(1 + 25)`
= `\sqrt(26)`
= 5.099
Distance between points (4, 3) and (3, -2) is 5.099
Distance between two points calculator uses coordinates of two points `A(x_A,y_A)` and `B(x_B,y_B)` in the two-dimensional Cartesian coordinate plane and find the length of the line segment `\overline{AB}`.
It’s an online Geometry tool requires coordinates of 2 points in the two-dimensional Cartesian coordinate plane.
It is necessary to follow the next steps:
For any two points there is exactly one line segment connecting them. The distance between two points is the length of the line segment connecting them. Note that the distance between two points is always positive. Segments that have equal length are called congruent segments.
Distance between 2 Points | |
---|---|
(xA, yA) and (xB, yB) | Distance |
(1, 2) and (3, 4) | 2.8284 |
(1, 3) and (-2, 9) | 6.7082 |
(1, 2) and (5, 5) | 5 |
(1, 2) and (7, 6) | 7.2111 |
(1, 1) and (7, -7) | 10 |
(13, 2) and (7, 10) | 10 |
(1, 3) and (5, 0) | 5 |
(1, 3) and (5, 6) | 5 |
(9, 6) and (2, 2) | 8.0623 |
(5, 7) and (7, 7) | 2 |
(8, 2) and (3, 8) | 7.8102 |
(8, -3) and (4, -7) | 5.6569 |
(8, 2) and (6, 1) | 2.2361 |
(-6, 8) and (-3, 9) | 3.1623 |
(7, 11) and (-1, 5) | 10 |
(-6, 5) and (-3, 1) | 5 |
(-6, 7) and (-1, 1) | 7.8102 |
(5, -4) and (0, 8) | 13 |
(5, -8) and (-3, 1) | 12.0416 |
(-5, 4) and (2, 6) | 7.2801 |
(4, 7) and ( 2, 2) | 5.3852 |
(4, 2) and ( 8, 5) | 5 |
(4, 6) and (3, 7) | 1.4142 |
(-3, 7) and (8, 6) | 11.0454 |
(-3, 4) and (5, 4) | 8 |
(-3, 2) and (5, 8) | 10 |
(-3, 4) and (1, 6) | 4.4721 |
(-2, 4) and (3, 9) | 7.0711 |
(-2, 4) and (4, 7) | 6.7082 |
(-2, 5) and (5, 2) | 7.6158 |
(-12, 1) and (12, -1) | 24.0832 |
(-1, 5) and (0, 4) | 1.4142 |
(-1, 4) and (4, 1) | 5.831 |
(0, 1) and (4, 4) | 5 |
(0, 5) and (12, 3) | 12.1655 |
(0, 1) and (6, 3.5) | 6.5 |
(0, 8) and (4, 5) | 5 |
(0, 0) and (3, 4) | 5 |
(0, 0) and (1, 1) | 1.4142 |
(0, 1) and (4, 4) | 5 |
(0, 5) and (12, 3) | 12.1655 |
(2, 3) and (5, 7) | 5 |
(2, 5) and (-4, 7) | 6.3246 |
(2, 3) and (1, 7) | 4.1231 |
(2, 8) and (5, 3) | 5.831 |
(3, 2) and (-1, 4) | 4.4721 |
(3, 12) and (14, 2) | 14.8661 |
(3, 7) and (6, 5) | 3.6056 |
(3, 4) and (0, 0) | 5 |
The length of a segment is usually denoted by using the endpoints without an overline. For instance, the `\text{length of AB}` is denoted by `\overline{AB}` or sometimes `m\overline{AB}`. A ruler is commonly used to find the the distance between two points. If we place the `0` mark at the left endpoint, and the mark on which the other endpoint falls on is the distance between two points. In general, we do not need to measure from the 0 mark. By the ruler postulate, the distance between two points is the absolute value between the numbers shown on the ruler. On the other hand, if two points `A and B` are on the x-axis, i.e. the coordinates of `A and B` are `(x_A,0)` and `(x_B,0)` respectively, then the distance between two points `AB = |x_B −x_A|`. The same method can be applied to find the distance between two points on the y-axis. The formula for the distance between two points in two-dimensional Cartesian coordinate plane is based on the Pythagorean Theorem. So, the Pythagorean theorem is used for measuring the distance between any two points `A(x_A,y_A)` and `B(x_B,y_B)`
If we compare the lengths of two or more line segments, we use the formula for the distance between two points. We usually use the distance formula for finding the length of sides of polygons if we know coordinates of their vertices. In this case, we can explore the nature of polygons. It can also help us for finding the area and perimeter of polygon.
Length between two points calculator is used in almost all fields of mathematics. For example, the distance between two complex numbers `z_1 = a + ib` and `z_2 = c + id` in the complex plane is the distance between points `(a,b) and (c,d)`, i.e.
Practice Problem 1:
Starting at the same point, Michael and Ann walked. Michael walked 5 miles north and 2 miles west, while Ann walked 7 miles east and 2 miles south. How far apart are them?
Practice Problem 2:
Find the distance between points `E and F.`