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Perpendicular Bisector Equation:
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The perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a 90-degree angle. The equation follows the point-slope form: \( y - y_m = m_{\perp} (x - x_m) \), where \( (x_m, y_m) \) is the midpoint and \( m_{\perp} \) is the perpendicular slope.
The calculator uses the perpendicular bisector equation:
Where:
Explanation: The calculator first finds the midpoint between two points, calculates the slope of the original line segment, then determines the perpendicular slope to construct the bisector equation.
Details: Perpendicular bisectors are fundamental in geometry, used in constructions, finding circumcenters of triangles, and solving various geometric problems involving equidistance and right angles.
Tips: Enter the coordinates of two distinct points. The calculator will compute and display the equation of the perpendicular bisector in point-slope form.
Q1: What if the two points are identical?
A: The calculator requires two distinct points to form a valid line segment. Identical points will not produce a meaningful result.
Q2: What does "undefined" slope mean?
A: An undefined slope occurs when the line is vertical. In this case, the perpendicular bisector will be a horizontal line.
Q3: Can this calculator handle decimal coordinates?
A: Yes, the calculator accepts and processes decimal coordinates with precision.
Q4: What is the practical application of perpendicular bisectors?
A: They are used in navigation, computer graphics, architectural design, and various engineering applications where equidistant points from two locations are needed.
Q5: How accurate are the calculations?
A: The calculator provides high precision results, typically rounded to 4 decimal places for clarity.