Distance Between 3 Points Calculator Slope

Distance and Slope Formulas:

\[ Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ Slope = \frac{y_2 - y_1}{x_2 - x_1} \]

Point 1

X1:

Y1:

Point 2

X2:

Y2:

Point 3

X3:

Y3:

Results

Distance between Point 1 and Point 2: Slope between Point 1 and Point 2: Distance between Point 2 and Point 3: Slope between Point 2 and Point 3: Distance between Point 1 and Point 3: Slope between Point 1 and Point 3:

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1. What is Distance and Slope Calculation?

Distance calculation measures the straight-line distance between two points in a coordinate plane, while slope calculation determines the steepness and direction of the line connecting two points.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ Slope = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

\( (x_1, y_1) \) — Coordinates of the first point
\( (x_2, y_2) \) — Coordinates of the second point
\( \Delta x \) — Difference in x-coordinates
\( \Delta y \) — Difference in y-coordinates

Explanation: The distance formula is derived from the Pythagorean theorem, while the slope formula calculates the ratio of vertical change to horizontal change.

3. Importance of Distance and Slope Calculation

Details: These calculations are fundamental in geometry, physics, engineering, computer graphics, and navigation. They help determine relationships between points in space and are essential for various analytical and practical applications.

4. Using the Calculator

Tips: Enter the coordinates for three points in the coordinate plane. The calculator will compute distances and slopes between all point pairs (1-2, 2-3, and 1-3). All values must be valid numerical coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What does an undefined slope mean?
A: An undefined slope occurs when the line is vertical (x-coordinates are equal), making the denominator zero in the slope formula.

Q2: Can I use negative coordinates?
A: Yes, the calculator works with both positive and negative coordinates in all quadrants of the coordinate plane.

Q3: What is the unit of distance measurement?
A: The distance is in the same units as the coordinate system. If coordinates are in meters, distance will be in meters.

Q4: How accurate are the calculations?
A: The calculator provides results with 4 decimal places precision, suitable for most educational and practical applications.

Q5: Can I calculate distances in 3D space?
A: This calculator is designed for 2D coordinates. For 3D distances, an extended formula including z-coordinates would be needed.