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What is the perpendicular bisector equation of a line segment with endpoints of p q and 7p 3q?
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
What else can I help you with?
What is the perpendicular bisector theorem?
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.
If a point lies on the perpendicular bisector of a segment then the point is always equidistant from the endpoints of the segment?
true
What is the difference between a perpendicular bisector and a angle 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.
Which of these is the definition of a perpendicular bisector?
a line or segment that is perpendicular to the given segment and divides it into two congruent segments
What is right bisector in math?
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).
If a point is equidistant from the endpoints of the segment then it is?
on the perpendicular bisector of the segment.
Are any points on the perpendicular bisector of a segment equally distant from the 2 endpoints?
All of the points on a perpendicular bisector are equidistant from the endpoints of the segment.
What is the perpendicular bisector theorem?
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.
If a point is equidistant from the endpoints of a segment then it is on?
on the perpendicular bisector of the segment.
If a point on the perpendicular bisector of a segment, then it is?
Equidistant from the endpoints of the segment.
What statement describes the points on the perpendicular bisector?
The points on the perpendicular bisector of a segment are equidistant from the segment's endpoints. This means that if you take any point on the perpendicular bisector, it will be the same distance from both endpoints of the segment. Additionally, the perpendicular bisector is a line that divides the segment into two equal parts at a right angle.
What is the perpendicluar bisector therom?
The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of that segment. Conversely, if a point is equidistant from the endpoints of a segment, it lies on the perpendicular bisector of that segment. This theorem is a fundamental concept in geometry, often used in constructions and proofs.
Which equation is the perpendicular bisector of the line segment with endpoints -2 4 and 6 8?
Endpoints: (-2, 4) and (6, 8) Slope: 1/2 Perpendicular slope: -2 Midpoint: (2, 6) Perpendicular bisector equation: y = -2x+10
If a point is on the perpendicular bisector of a segment?
then it is equidistant from the endpoints of the segment- apex
What is the perpendicular bisector equation of the line segment whose endpoints are at 2 9 and 9 2?
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
How do you write the converse of perpendicular bisector theorem easier to understand?
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.
State the Perpendicular Bisector Theorem and its converse as a biconditional?
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.
