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Q: Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,-3) and (7,-7)?

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All of the points on a perpendicular bisector are equidistant from the endpoints of the segment.

on the perpendicular bisector of the segment.

then it is equidistant from the endpoints of the segment- apex

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 :))

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.

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.

true

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

Endpoints: (-2, 4) and (6, 8) Slope: 1/2 Perpendicular slope: -2 Midpoint: (2, 6) Perpendicular bisector equation: y = -2x+10

true

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

Endpoints: (-1, 3) and (-2, -5) Midpoint: (-3/2, -1) Slope: 8 Perpendicular slope: -1/8 Perpendicular bisector equation: y --1 = -1/8--3/2 => y = -1/8x -19/16

8

The distance will be length of the line divided by 2 because the perpendicular bisector cuts through the line at its centre and at right angles

Endpoints: (-7, -3) and (-1, -4) Midpoint: (-4, -3.5) Slope: (-3--4)/(-7--1) = -1/6 Perpendicular slope: 6 Perpendicular bisector equation: y--3.5 = 6(x--4) => y = 6x+20.5

Endpoints: (-4, -10) and (8, -1) Midpoint: (2, -5.5) Slope: 3/4 Perpendicular slope: -4/3 Perpendicular equation: y --5.5 = -4/3(x-2) => 3y = -4x -8.5 Perpendicular bisector equation in its general form: 4x+3y+8.5 = 0

End points: (-7, -3) and (-1, -4) Midpoint: (-4, -3.5) Slope: -1/6 Perpendicular slope: 6 Perpendicular bisector equation: y--3.5 = 6(x--4) => y = 6x+20.5

The description seems a bit confusing (to me) but it sounds like it could be a perpendicular bisector of a side of a triangle.

Equidistant from the two sides of an angle.

The perpendicular bisector of a line segment AB is the straight line perpendicular to AB through the midpoint of AB.

Perpendicular Bisector

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.