Perpendicular Bisector

Front

What is a perpendicular bisector?

Back

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

Front

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

Back

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

If a line segment AB has a midpoint M, what is the relationship between AM and MB?

Back

AM = MB; the lengths are equal because M is the midpoint.

Front

How can you determine if a line is a perpendicular bisector?

Back

To determine if a line is a perpendicular bisector, check if it is perpendicular to the segment and passes through the midpoint.

Front

What is the formula for finding the midpoint of a segment with endpoints A(x1, y1) and B(x2, y2)?

Back

Front

If the coordinates of points A and B are (2, 3) and (6, 7), what is the length of segment AB?

Back

Front

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

Back

The perpendicular bisector of a side of a triangle is the locus of points equidistant from the endpoints of that side.

Front

How do you find the equation of a perpendicular bisector given two points?

Back

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

Front

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

Back