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.
Endpoints: (-2, 4) and (6, 8) Slope: 1/2 Perpendicular slope: -2 Midpoint: (2, 6) Perpendicular bisector equation: y = -2x+10
then it is equidistant from the endpoints of the segment- apex
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