Redo 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

How do you find the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M is given by the formula M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If a line segment AB is bisected at point C, what can be said about AC and BC?

Back

AC = BC; they are equal in length.

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 the coordinates of points A(2, 3) and B(8, 7) are given, what is the length of segment AB?

Back

Front

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

Back

Front

If point P lies on the perpendicular bisector of segment XY, what can be concluded about the distances PX and PY?

Back

PX = PY; point P is equidistant from points X and Y.

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 is on the perpendicular bisector of a segment?

Back

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

Front

What is the equation of a line that is perpendicular to the line y = 2x + 3?

Back

The slope of the perpendicular line is -1/2, so the equation can be written as y = -1/2x + b, where b is the y-intercept.