A line with slope m has a perpendicular with slope m' such that:
mm' = -1
→ m' = -1/m
The line segment with endpoints (p, q) and (7p, 3q) has slope:
slope = change in y / change in x
→ m = (3q - q)/(7p - p) = 2q/6p = q/3p
→ m' = -1/m = -1/(q/3p) = -3p/q
The perpendicular bisector goes through the midpoint of the line segment which is at the mean average of the endpoints:
midpoint = ((p + 7p)/2, (q + 3q)/2) = (8p/2, 4q/2) = (4p, 2q)
A line through a point (X, Y) with slope M has equation:
y - Y = M(x - x)
→ perpendicular bisector of line segment (p, q) to (7p, 3q) has equation:
y - 2q = -3p/q(x - 4p)
→ y = -3px/q + 12p² + 2q
→ qy = 12p²q + 2q² - 3px
Another Answer: qy =-3px +12p^2 +2q^2
If a point is on the perpendicular bisector of a segment, then it is equidistant, or the same distance, from the endpoints of the segment.
true
A perpendicular bisector is a line that divides a given line segment into halves, and is perpendicular to the line segment. An angle bisector is a line that bisects a given angle.
a line or segment that is perpendicular to the given segment and divides it into two congruent segments
A right bisector of a line segment, is better know as a perpendicular bisector. It is a line that divides the original line in half and is perpendicular to it (makes a right angle).
on the perpendicular bisector of the segment.
All of the points on a perpendicular bisector are equidistant from the endpoints of the segment.
If a point is on the perpendicular bisector of a segment, then it is equidistant, or the same distance, from the endpoints of the segment.
on the perpendicular bisector of the segment.
Equidistant from the endpoints of the segment.
then it is equidistant from the endpoints of the segment- apex
Endpoints: (-2, 4) and (6, 8) Slope: 1/2 Perpendicular slope: -2 Midpoint: (2, 6) Perpendicular bisector equation: y = -2x+10
Endpoints: (2, 9) and (9, 2) Midpoint: (5.5, 5.5) Slope of line segment: -1 Perpendicular slope: 1 Perpendicular bisector equation: y-5.5 = 1(x-5.5) => y = x
The converse of perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Biconditional Statement for: Perpendicular Bisector Theorem: A point is equidistant if and only if the point is on the perpendicular bisector of a segment. Converse of the Perpendicular Bisector Theorem: A point is on the perpendicular bisector of the segment if and only if the point is equidistant from the endpoints of a segment.
Converse of the Perpendicular Bisector Theorem - if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.Example: If DA = DB, then point D lies on the perpendicular bisector of line segment AB.you :))
Endpoints: (-1, -6) and (5, -8) Midpoint: (2, -7) Slope: -1/3 Perpendicular slope: 3 Perpendicular bisector equation: y - -7 = 3(x -2) => y = 3x -13