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

If a point M lies on the perpendicular bisector of segment PQ, what can be said about the distances PM and QM?

Back

PM = QM; any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

How do you find the midpoint of a segment?

Back

The midpoint can be found by averaging the x-coordinates and y-coordinates of the endpoints. For endpoints A(x1, y1) and B(x2, y2), the midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope m, the other line's slope will be -1/m.

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 can you determine if two lines are perpendicular using their slopes?

Back

If the product of the slopes of two lines is -1, then the lines are perpendicular.

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, and it can be used to find the circumcenter of the triangle.

Front

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

Back

Front

What does it mean for a line to bisect another line segment?

Back

To bisect a line segment means to divide it into two equal parts.

Front

How do you construct a perpendicular bisector using a compass and straightedge?

Back

1. Draw the line segment. 2. With the compass, draw arcs from both endpoints that intersect above and below the segment. 3. Draw a line through the intersection points of the arcs.