What is the distance formula in geometry?
It’s an equation used to find the straight-line distance between two points in a coordinate system.
What is the distance formula in coordinate geometry?
It finds the length of the line segment connecting two points, $(x_1, y_1)$ and $(x_2, y_2)$, on a coordinate plane.
How does the distance formula work?
It applies the Pythagorean theorem to the horizontal and vertical distances between the two points.
Which is the distance formula?
The general formula for two points in a 2D plane is $d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$
When is the distance formula used?
It’s used when you need to find the shortest path or length between two specific locations (points) on a map or graph.
Where is the distance formula used?
It’s used in geometry, physics, navigation, and any field dealing with coordinate locations.
Why is the distance formula used?
It provides an exact, measurable length for the separation between two points.
Can the distance formula be a decimal?
Yes, the resulting distance can be a decimal number (a non-integer).
Can distance formula be negative?
No, distance is a length measurement and is always zero or a positive value.
How is the distance formula related to the Pythagorean theorem?
The distance formula is directly derived from the Pythagorean theorem, $a^2 + b^2 = c^2$
Can the distance formula be derived from the Pythagorean theorem?
Yes, by treating the distance as the hypotenuse ($c$) of a right triangle and the differences in coordinates as the legs ($a$ and $b$).
Why is the distance formula related to the Pythagorean theorem?
Because the two points and their horizontal/vertical differences form a right-angled triangle.
Why is the distance formula squared?
The differences in the $x$ and $y$ coordinates are squared (e.g., $(x_2 – x_1)^2$) to ensure the resulting values are always positive before they are added.
Who invented the distance formula?
It is not attributed to a single inventor; it developed as a result of the work of mathematicians like Pythagoras and René Descartes (who created coordinate geometry).
How can the distance formula be used in real life?
It’s used in GPS systems to calculate travel distance, in construction for layout, and in sports for tracking movement.
What is distance formula in physics?
In basic physics, it still refers to the geometric distance, but other formulas like $d = vt$ (distance = speed $\times$ time) are also common.
Distance formula when speed and time is given?
Use the formula: Distance = Speed $\times$ Time ($d = vt$).
Distance formula when two points are given?
Use the standard distance formula: $d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$
What is the 3 dimensional distance formula?
It extends the 2D formula by adding a $z$ component: $d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2}$
Distance formula vs midpoint formula?
The distance formula finds the length between two points; the midpoint formula finds the coordinates of the center point between them.