To find the distance between two points in a 2D coordinate plane, you use the distance formula derived from the Pythagorean theorem. If the points are (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2), the distance ddd between them is given by:
d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2−x1)2+(y2−y1)2
Steps to Calculate Distance:
- Identify the coordinates of the two points.
- Subtract the x-coordinates and square the result.
- Subtract the y-coordinates and square the result.
- Add these squared differences.
- Take the square root of the sum to get the distance.
Example: Find the distance between points A(2,3)A(2,3)A(2,3) and B(5,7)B(5,7)B(5,7):
d=(5−2)2+(7−3)2=32+42=9+16=25=5d=\sqrt{(5-2)^2+(7-3)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5d=(5−2)2+(7−3)2=32+42=9+16=25=5
This means the distance between points A and B is 5 units
. For points in 3D space (x1,y1,z1)(x_1,y_1,z_1)(x1,y1,z1) and (x2,y2,z2)(x_2,y_2,z_2)(x2,y2,z2), the formula extends to:
d=(x2−x1)2+(y2−y1)2+(z2−z1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}d=(x2−x1)2+(y2−y1)2+(z2−z1)2
This method is widely used in geometry, navigation, engineering, and many practical applications
. If you are dealing with geographic coordinates (latitude and longitude), a different formula such as the Haversine formula is used to calculate the great-circle distance on the Earth's surface
