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Only 1 line can be drawn perpendicular to a given line at a given point?
Wiki User
∙ 13y ago
Yes (in a Euclidean plane)..
Wiki User
∙ 13y ago
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What postulate or theorem guarantees that there is only one line that can be constructed perpendicular to a given line from a given point not on the line?
It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "
What is perpendicular to y equals 3x plus 8?
3y + x = k where k is some constant which can only be determined if a point on it is known. There is no such point given.
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
Is it possible to construct an infinite number of lines that are perpendicular to any given line?
Yes, but only in principle. In practice, you won't live long enough. Putting it in more positive terms: No matter how many lines have already been drawn perpendicular to a given line [segment], there's always enough room for a lot more of them.
How many points do perpendicular lines share?
Perpendicular lines will only share one point: the point of intersection, where the two lines meet.
What postulate or theorem guarantees that there is only one line that can be constructed perpendicular to a given line from a given point not on the line?
It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "
How many planes can be perpendicular to a given line at a given point?
Only one
In space how many planes can be perpendicular to a given line at a given point?
only 1
How many perpendicular can we draw to a line from a given point outside the line?
In a Euclidean plane, only one.
What is needed to determine a line?
Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.
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.
What is perpendicular to y equals 3x plus 8?
3y + x = k where k is some constant which can only be determined if a point on it is known. There is no such point given.
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
How many circles can pass through two given points?
It takes 3 non collinear points to define one specific circle. With only two points an infinite number of circles can be drawn. Proof: Given two points A, B draw the line between them. Then find the perpendicular bisector of the line AB. Any point on the perpendicular bisector is equidistant from the two original points, A and B. A circle with center C and radius AC will then pass through points A and B. There are infinite point C's on the perpendicular bisector so there are infinite circles. Given three points A, B and D you can find the perpendicular bisector for line segements AB and then the perpendicular bisector fof line segment BC. The two perpedicular bisectors will not be parallel because the points A, B and D are non collinear. This means the two perpeniducar bisectors will intercept at only one point C(like any two intercepting lines). This point C is equidistant from points A, B, and D. A circle with center C and radius AC will then pass through all three of the points. Since there is only one point C that lies on both perpendicular bisectors, there is only one circle possible.
Is it possible to construct an infinite number of lines that are perpendicular to any given line?
Yes, but only in principle. In practice, you won't live long enough. Putting it in more positive terms: No matter how many lines have already been drawn perpendicular to a given line [segment], there's always enough room for a lot more of them.
How many points do perpendicular lines share?
Perpendicular lines will only share one point: the point of intersection, where the two lines meet.
Do perpendicular lines intersect in at least two points?
Perpendicular lines intersect at one point only.
