Perpendicular Bisectors

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How do you find the length of a segment given its endpoints?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between a point on the perpendicular bisector and the endpoints of the segment?

Back

Any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

How can you determine if a point lies on the perpendicular bisector of a segment?

Back

Calculate the distances from the point to each endpoint; if they are equal, the point lies on the bisector.

Front

What is the midpoint of a segment?

Back

The midpoint is the point that divides the segment into two equal lengths, calculated as ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the slope of a line perpendicular to another line with slope m?

Back

The slope of a line perpendicular to another line with slope m is -1/m.

Front

How do you write the equation of a perpendicular bisector given two endpoints?

Back

1. Find the midpoint of the segment. 2. Determine the slope of the segment. 3. Use the negative reciprocal of that slope for the perpendicular slope. 4. Use point-slope form to write the equation.

Front

What is the significance of the perpendicular bisector in triangle construction?

Back

The perpendicular bisector of a side of a triangle helps locate the circumcenter, which is equidistant from all vertices.

Front

How can you apply the Pythagorean theorem in problems involving perpendicular bisectors?

Back

The Pythagorean theorem can be used to find distances and verify right angles in triangles formed by the bisector.

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²).