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Construction of Perpendicular Through a Point not on it Video Lecture - Class 6

FAQs on Construction of Perpendicular Through a Point not on it Video Lecture - Class 6

1. What is the construction of a perpendicular through a point not on it?

Ans. The construction of a perpendicular through a point not on it involves drawing a line that is perpendicular to another line, passing through a given point that is not on the line.

2. How do you construct a perpendicular through a point not on it?

Ans. To construct a perpendicular through a point not on it, follow these steps: 1. Draw a line passing through the given point. 2. From the given point, draw two arcs on opposite sides of the line. 3. With the same radius as the previous arcs, draw two more arcs intersecting the previous arcs. 4. Draw a line connecting the two intersection points. This line is perpendicular to the given line and passes through the given point.

3. Why is it important to construct a perpendicular through a point not on it?

Ans. Constructing a perpendicular through a point not on it is important because it helps in various geometric constructions and calculations. It allows us to find the shortest distance from a point to a line, determine the perpendicular bisector of a line segment, and construct right angles in various geometrical figures.

4. Can you construct a perpendicular through any point on a line?

Ans. No, we cannot construct a perpendicular through any point on a line. A perpendicular can only be drawn through a point that is not on the line. If the point lies on the line, the perpendicular would coincide with the line itself.

5. What are some practical applications of constructing a perpendicular through a point not on it?

Ans. Some practical applications of constructing a perpendicular through a point not on it include: - Determining the shortest distance from a point to a line, which is useful in navigation and finding the nearest path. - Constructing perpendicular bisectors, which are used in dividing a line segment into two equal parts. - Creating right angles in various architectural and engineering designs, such as constructing perpendicular walls or beams.

Text Transcript from Video

given a line and a point not on that
line construct a line through that point
which is perpendicular to the given line
so here's our given line and getting
point put your compass point on the
point P open up your compass and make an
arc so that intersects the given line in
two different places label those two
places a and B and essentially what
we're going to do is construct now a
perpendicular bisector of the segment a
B because of the fact that P is
equidistant to a and B already we know
that P has to lie on the perpendicular
bisector of segment a B so open your
compass over halfway between a and B and
make an arc and then put your compass
point over on point a keeping the same
radius for your compass on make another
arc use the two intersection points of
those two arcs and construct a line
through those two points the line now
that you've constructed is the
perpendicular bisector of a B but more
importantly it is a line that goes
through point P that is perpendicular to
your given line a B

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Sep 25, 2025 Last updated

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