To find the distance between two points on a coordinate plane, you can use the distance formula derived from the Pythagorean theorem. Given two points (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2), the distance ddd between them is calculated as:
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 the distance:
- Identify the coordinates of the two points.
- Subtract the x-coordinates: x2−x1x_2-x_1x2−x1.
- Subtract the y-coordinates: y2−y1y_2-y_1y2−y1.
- Square both differences.
- Add the squared values.
- Take the square root of the sum to get the distance.
Example:
For 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 formula can also be extended to three dimensions with points (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):
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 various real-world applications
