Geometry Perpendicular Bisectors

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?

Back

The midpoint can be found using the formula: Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) for endpoints (x1, y1) and (x2, y2).

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 endpoints A(2, 3) and B(4, 7), what is the midpoint?

Back

Midpoint M = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

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 determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

If the coordinates of points A and B are (1, 2) and (5, 6), what is the length of segment AB?

Back

Length of AB = @@ ext{Distance} = \\sqrt{(5-1)^2 + (6-2)^2} = \\sqrt{16 + 16} = \\sqrt{32} = 4 ext{√}2.$$

Front

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

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the equation of a perpendicular bisector?

Back

To find the equation of a perpendicular bisector, first find the midpoint of the segment, then use the negative reciprocal of the slope of the segment to write the equation.

Front

What is the distance formula?

Back

The distance formula is given by: Distance = @@ ext{Distance} = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$$