6.1 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 midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2)?

Back

The midpoint M is given by M = (\frac{x1 + x2}{2}, \frac{y1 + y2}{2}).

Front

If line segment AB has endpoints A(2, 3) and B(6, 7), what is the midpoint?

Back

The midpoint M is M = (\frac{2 + 6}{2}, \frac{3 + 7}{2}) = (4, 5).

Front

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

Back

The slope of a line perpendicular to a line with slope m is -\frac{1}{m}.

Front

If the slope of line AB is 2, what is the slope of the perpendicular bisector of AB?

Back

The slope of the perpendicular bisector is -\frac{1}{2}.

Front

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

Back

A point lies on the perpendicular bisector if it is equidistant from the endpoints of the segment.

Front

What is the equation of a line in point-slope form?

Back

The equation of a line in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

Given the points A(1, 2) and B(3, 4), find the equation of the perpendicular bisector.

Back

1. Find the midpoint: M = (2, 3). 2. Find the slope of AB: m = 1. 3. Slope of perpendicular bisector = -1. 4. Equation: y - 3 = -1(x - 2) or y = -x + 5.

Front

What is the distance formula between two points A(x1, y1) and B(x2, y2)?

Back

The distance d is given by d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Front

Calculate the distance between points A(1, 1) and B(4, 5).

Back

d = \sqrt{(4 - 1)^2 + (5 - 1)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.