Calculator Input
Example Data Table
| X1 | Y1 | X2 | Y2 | Midpoint | Perpendicular Bisector |
|---|---|---|---|---|---|
| 2 | 3 | 8 | 9 | (5, 6) | y = -x + 11 |
| 0 | 0 | 6 | 0 | (3, 0) | x = 3 |
| 4 | 1 | 4 | 7 | (4, 4) | y = 4 |
Formula Used
For two points A(x1, y1) and B(x2, y2), the midpoint is:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
The original segment slope is:
m = (y2 - y1) / (x2 - x1)
The perpendicular slope is the negative reciprocal:
m⊥ = -1 / m
The general equation is found from the equal distance rule:
2(x2 - x1)x + 2(y2 - y1)y + x1² + y1² - x2² - y2² = 0
How to Use This Calculator
- Enter the x and y values for the first point.
- Enter the x and y values for the second point.
- Select the decimal precision for the final result.
- Press the calculate button.
- Review the result shown above the form.
- Use the graph to check the line direction visually.
- Download the result as CSV or PDF if needed.
Perpendicular Bisector Guide
What It Means
A perpendicular bisector is a line with two jobs. It cuts a segment into two equal parts. It also meets that segment at a right angle. This calculator helps you build that line from any two coordinate points.
Midpoint Step
The first step is the midpoint. The midpoint is the center of the segment. It uses the average of both x values and both y values. Every perpendicular bisector must pass through this center point.
Slope Step
The second step is the segment slope. Slope shows how fast the segment rises compared with its run. The perpendicular slope is the negative reciprocal of that value. When the original segment is horizontal, the bisector is vertical. When the original segment is vertical, the bisector is horizontal.
Equation Forms
The tool also gives the general equation. That form is useful for checking work. It comes from equal distance rules. Any point on the bisector is the same distance from the first point and the second point. This idea makes the line important in geometry, analytic proof, and circle construction.
Advanced Review
Advanced outputs make the result easier to review. You can see the midpoint, original slope, perpendicular slope, length, slope-intercept form, and standard form. A graph shows the segment and its bisector together. The example table shows sample input data and expected equation styles.
Practical Use
Use the calculator when solving homework, checking coordinate geometry, or preparing teaching material. It reduces manual errors. It also shows each important value clearly. Exports help you keep records for class notes or reports.
Layout Checks
The calculation is also useful in design tasks. A perpendicular bisector can help locate a center point between two anchors. It can support layout checks, map work, and simple construction planning. Because the method is based on coordinates, it works with positive, negative, and decimal values.
Graph Review
The graph is not just decorative. It helps confirm direction. The segment and bisector should cross at the midpoint. Their intersection should form a square corner. If the picture looks wrong, review the entered coordinates and units. Then compare the equation forms before exporting results.
Accuracy Tip
For best accuracy, use consistent units. Round only after checking the exact values. Small rounding changes can alter the displayed equation.
FAQs
1. What is a perpendicular bisector?
It is a line that cuts a segment into two equal parts and meets it at a right angle.
2. What inputs are required?
You need two coordinate points. Enter x and y values for each endpoint of the segment.
3. Why is the midpoint important?
The perpendicular bisector always passes through the midpoint. That point anchors the final equation.
4. What happens if the segment is horizontal?
The perpendicular bisector becomes a vertical line. Its equation uses the midpoint x value.
5. What happens if the segment is vertical?
The perpendicular bisector becomes a horizontal line. Its equation uses the midpoint y value.
6. Why does the calculator show general form?
General form is useful for proofs, checking substitutions, and comparing equations without solving for y.
7. Can I use decimal coordinates?
Yes. The calculator accepts decimal, negative, and positive coordinate values for both points.
8. What do the export buttons do?
The CSV button downloads tabular results. The PDF button downloads a clean summary of the calculation.