Right Triangle Calculator Using Points

Distance Formula:

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

Point A (x1):

Point A (y1):

Point B (x2):

Point B (y2):

Point C (x3):

Point C (y3):

Is Right Triangle:

Side AB Length:

Side BC Length:

Side AC Length:

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1. What is a Right Triangle Calculator Using Points?

Definition: This calculator determines if three given points form a right triangle and calculates its properties.

Purpose: It helps in geometry analysis by verifying right angles and computing triangle measurements from coordinate points.

2. How Does the Calculator Work?

The calculator uses the distance formula:

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

And checks the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

Where:

\( a, b \) — Legs of the triangle
\( c \) — Hypotenuse (longest side)
\( (x_1,y_1), (x_2,y_2), (x_3,y_3) \) — Coordinate points

3. Importance of Right Triangle Calculation

Details: Right triangles are fundamental in geometry, trigonometry, and practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter the x,y coordinates for three points. The calculator will determine if they form a right triangle and show all measurements.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the right angle detection?
A: It uses floating-point precision with a tolerance of 0.0001 to account for rounding errors.

Q2: What units does this calculator use?
A: The units match your input coordinates (e.g., meters, feet). Results are in the same unit squared for area.

Q3: Can I use this for 3D coordinates?
A: No, this calculator only works with 2D coordinates. For 3D, you would need to include z-coordinates.

Q4: What if my points form a straight line?
A: The calculator will show "No" for right triangle and display the distances between points.

Q5: How is the area calculated?
A: For right triangles, area = (leg1 × leg2) / 2. Only shown when points form a valid right triangle.