Redo 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.

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

A point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.

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

The distance formula is used to find the distance between two points in a coordinate plane, given by: Distance = $$\text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$ .

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

The slope of the perpendicular bisector is the negative reciprocal of the slope of the segment it bisects.

To determine if a point lies on the perpendicular bisector, check if it is equidistant from the segment's endpoints.

The slope (m) between two points (x1, y1) and (x2, y2) is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

Slope = $$\frac{6 - 2}{5 - 1} = \frac{4}{4} = 1$$ .