Perpendicular Bisector Theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

Define 'perpendicular bisector'.

Back

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

Front

If point D is on the perpendicular bisector of segment AB, what can be said about the distances AD and DB?

Back

AD = DB; point D is equidistant from points A and B.

Front

How do you find the midpoint of a segment?

Back

To find the midpoint of a segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((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.

Front

If a line segment has endpoints (2, 3) and (4, 7), what is the length of the segment?

Back

Length = √((x2 - x1)² + (y2 - y1)²) = √((4 - 2)² + (7 - 3)²) = √(4 + 16) = √20 = 2√5.

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

If a point is equidistant from two points, what can be said about its location?

Back

The point lies on the perpendicular bisector of the segment connecting the two points.

Front

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

Back

The perpendicular bisector of a side of a triangle helps in finding the circumcenter, which is the center of the circumcircle.

Front

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

Back

Calculate the distances from the point to the endpoints of the segment; if the distances are equal, the point lies on the perpendicular bisector.