Tag: drawing of different geometrical figures

Questions Related to drawing of different geometrical figures

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

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

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Correct Option: A
Explanation:

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

A vertex of square is $(3,4)$ and diagonal's equation is given by $x+2y=1$,then the second diagonal which passes through given vertex will be 

maths drawing of different geometrical figures constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector

  1. $2x-y+2=0$

  2. $x+2y=11$

  3. $2x-y=2$

  4. None of these

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Correct Option: C
Explanation:
Diagonals of Square are perpendicular bisector of each other.

$x+2y=1 \Rightarrow y=\dfrac{-x}{2}+\dfrac{1}{2}$

Comparing with $y=mx+c$ we have $slope=m _1=\dfrac{-1}{2}$

As diagonals are perpendicular, so

 $m _1\times m _2=-1$

$\dfrac{-1}{2}\times m _2=-1$

$m _2=2$

equation of other diagonal is $y=2x+c$

as this passes through $(3,4)$ it satifies the equation

$\Rightarrow 4=2(3)+c \Rightarrow c=-2$

Thus equation of diagonal $\equiv 2x-y-2=0$

Hence, the answer is option $C$

With ruler and compasses,we can bisect any given line segment.

maths drawing of different geometrical figures constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. True

  2. False

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Correct Option: A