Tag: construction of a perpendicular bisector

Questions Related to construction of a perpendicular bisector

$\overset \leftrightarrow{PQ}$ is perpendicular to $\overset \leftrightarrow{RS}$ is symbolically written as

maths drawing of different geometrical figures constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $\overset \leftrightarrow{PQ}\, \perp \, \overset \leftrightarrow{RS}$

  2. $\overset \leftrightarrow{PQ}\, \parallel \, \overset \leftrightarrow{RS}$

  3. $\overset \leftrightarrow{PQ}\, \neq \, \overset \leftrightarrow{RS}$

  4. $\overset \leftrightarrow{PQ}\, = \, \overset \leftrightarrow{RS}$

Show answer
Correct Option: A
Explanation:

$ \overleftrightarrow { PQ } $ is perpendicular to $ \overleftrightarrow { RS } $ is symbolically written as $ \overleftrightarrow { PQ } \bot  \overleftrightarrow { RS }  $

When two line segments meet at a point forming right angle they are said to be __________ to each other.

maths drawing of different geometrical figures constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. Parallel

  2. Perpendicular

  3. Equal

  4. None of the above

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Correct Option: B
Explanation:

When two line segments meet at a point forming right angle they are said to be perpendicular to each other.

$\displaystyle \overleftrightarrow {PQ}$ is perpendicular to $\displaystyle \overleftrightarrow {RS}$ is symbolically written as:

maths drawing of different geometrical figures constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $\displaystyle \overleftrightarrow {PQ}\perp \overleftrightarrow {RS}$

  2. $\displaystyle \overleftrightarrow {PQ}\parallel \overleftrightarrow{RS}$

  3. $\displaystyle \overleftrightarrow {PQ}\neq \overleftrightarrow{RS}$

  4. $\displaystyle \overleftrightarrow{PQ}= \overleftrightarrow {RS}$

Show answer
Correct Option: A
Explanation:

$ \overleftrightarrow { PQ } $ is perpendicular to $ \overleftrightarrow { RS } $ is symbolically written as $\overleftrightarrow { PQ } \bot  \overleftrightarrow { RS } $

When two lines are perpendicular to each other, the angle is said to be _______ angle.

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. acute

  2. right

  3. obtuse

  4. equal

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Correct Option: B
Explanation:

Two given lines are perpendicular means the angle between them is $90^o$, i.e. a right angle.

When a perpendicular is drawn to a given line, in what ratio is the line divided into?

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1:1$

  2. $1:2$

  3. $2:1$

  4. Cannot be said

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Correct Option: D
Explanation:

A line does not have a definite length.

Hence, when a perpendicular is drawn to the given line, nothing can be said about the ratio it gets divided into.

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the fourth step :

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
Explanation:

$1.$ Draw a line $XY$ and mark a point $P$ on it.

$2.$ Place one short side of the set square on the line $XY$.
$3.$ Move the set square along $XY$ so the other short side touches point $P$.
$4.$ Use the edge of the set square to draw a line through point $P$ .
So $2.$ is the fourth step.
Option $B$ is correct.

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the first step :

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

$1.$ Draw a line $XY$ and mark a point $P$ on it.

$2.$ Place one short side of the set square on the line $XY$.
$3.$ Move the set square along $XY$ so the other short side touches point $P$.
$4.$ Use the edge of the set square to draw a line through point $P$ .
So $3.$ is the first step.
Option $C$ is correct.

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the second step :

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: D
Explanation:

$1.$ Draw a line $XY$ and mark a point $P$ on it.

$2.$ Place one short side of the set square on the line $XY$.
$3.$ Move the set square along $XY$ so the other short side touches point $P$.
$4.$ Use the edge of the set square to draw a line through point $P$ .
So $4.$ is the second step.
Option $D$ is correct.

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the first step from the following.
1) Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $4$

  2. $3$

  3. $2$

  4. $1$

Show answer
Correct Option: C
Explanation:

The correct sequence is:

Step 1. Draw a line $L$ and consider a point $P$ outside the line.
Step 2. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step 3.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step 4. Draw line $PQ$
So the first step is $2$
Option $C$ is correct.

When a perpendicular is drawn to a given line and it also bisects it, then the perpendicular divides the line into

maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1:1$

  2. $1:2$

  3. $2:3$

  4. None of the above

Show answer
Correct Option: A
Explanation:

Bisects means division into two equal parts .

When a perpendicular is drawn to a given line and it also bisects it, then the perpendicular divides the line into
Thus the correct answer is $1: 1$