Perpendicular Bisector Theorem

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.

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

PA = PB; point P is equidistant from points A and B.

To find the midpoint of a segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

The slopes of two perpendicular lines are negative reciprocals of each other.

Length of AB = √((x2 - x1)² + (y2 - y1)²) = √((6 - 2)² + (7 - 3)²) = √(16 + 16) = √32 = 4√2.

It helps in constructing the circumcenter of a triangle, which is the point where the perpendicular bisectors of the sides intersect.

It is a right triangle, as it satisfies the Pythagorean theorem: 6² + 8² = 10².

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

Check if the distances from the point to the endpoints of the segment are equal.