Tag: construction related to lines

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Questions Related to construction related to lines

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Construct a line segment of length $4.6\ cm$. Divide this line into $2$ equal parts and find the length of each part.

  1. $2.0\ cm$
  2. $2.1\ cm$
  3. $2.2\ cm$
  4. $2.3\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
steps of construction :
1 . draw a line of length 4.6 cm using ruler .
2. Place the compass at one end of line segment.
3 . Adjust the compass to slightly longer than half the line segment length.
4. Draw arcs above and below the line.
 5 .Keeping the same compass width, draw arcs from other end of line.
6 . Place ruler where the arcs cross, and draw the line segment.
7. drawn line segment cuts the initial line segment  into two equal parts .
8. measure the bisected length using ruler thats comes out be $= \dfrac{1}{2} \times 4.6 = 2.3 cm$
Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Draw a line $AB=7.8\ cm$, what will be the $\dfrac{2}{3}$rd of $AB$.

  1. $11.7\ cm$
  2. $5.2\ cm$
  3. $3.9\ cm$
  4. $2.6\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Draw a line segment $AB$ of $7.8\ \ cm$ using ruler 

.$\dfrac{2}{3}AB=$ $=\dfrac { 2 }{ 3 } \times 7.8=5.2 \ cm$
Option $B$ is correct.

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Construct a line $AB=6.5\ cm$. What will be the $\dfrac{1}{5}$th of $AB$ ?

  1. $4.2\ cm$
  2. $3.5\ cm$
  3. $2.4\ cm$
  4. $1.3\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Draw a line segment $AB$ of length $6.5\ \ cm$

$\dfrac { 1 }{ 5 } AB=\dfrac { 1 }{ 5 } \times 6.5=1.3\ \ cm$
So option $D$ is correct.

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Draw a line $XY=13.6\ cm$. what will be the $\dfrac{1}{4}$th of $XY$ ?

  1. $6.8\ cm$
  2. $5.2\ cm$
  3. $3.4\ cm$
  4. $2.2\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Draw a line segment $XY$ of length $13.6\ \ cm$

$\dfrac { 1 }{ 4 } XY=\dfrac { 1 }{ 4 } \times 13.6=3.4\ \ cm$
Option $C$ is correct.

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Draw a line $PQ=9.6\ cm$. What will be the $\dfrac{1}{3}$rd of $PQ$ ?

  1. $3.2\ cm$
  2. $4.6\ cm$
  3. $2.4\ cm$
  4. $2.5\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Draw a line segment $PQ$ is length $9.6\ \ cm$ using a ruler.

$\dfrac { 1 }{ 3 } PQ=\dfrac { 1 }{ 3 } \times 9.6=3.2\ \ cm$
So option $A$ is correct.

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Steps of constructing a line segment equal to the length of given segment is written in jumbled form below:
1. Draw a line $l$. Mark a point $A$ on line $l$. Without changing compass's setting, place the compass at $A$.
2. Make an arc on the line $l$ which cuts $l$ at $B$. Now, $AB$ is a copy of $CD$.
3. Draw a line segment $CD$ of any length.
4. Fix the compass's end on $C$ and pencil on $D$. This gives the length of $CD$.

Which of the above comes first.

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Correct sequence is :

Step 1. Draw a line segment $CD$ of any length.
Step 2 .Fix the compass's end on $C$ and a pencil on $D$. This gives length $CD.$
Step 3. Draw a line $l$. Mark a point $A$ on line $l$.Without changing compass's setting place the compass at $A$
Step 4. Make an arc on the line $l$ whcih cuts $l$ at $B$  Now $AB$ is a copy of $CD$
So the first step is $3$
Option $C$ is correct.

Multiple choice maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

Choose the correct answer from the alternatives given.
Water is flowing at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank which is $50$ m long, $44$ m wide. The time taken (in hours) for the rise in the level of water in the tank to be $7$ cm is

  1. $2$
  2. $1\dfrac{1}{2}$
  3. $3$
  4. $2\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Water
flowed by the pipe in lh = $\pi r^2h$
= $\dfrac{22}{7} \times$ $\dfrac{7\times 7}{100\times100}$ $\times 5000 m^3 =77m^3$
Volume
of expected water in the tank = $\frac{50 \times 44 \times 7}{100} = 154
m^3$ 
Required
time= $154/77 = 2 hrs$.

Multiple choice maths basic geometrical concepts and shapes construction of line segment and circle of given radius construction related to lines constructing line segment

Four distinct points $(2K , 3K), (1 , 0), (0 , 1)$ and $(0 , 0)$ lie on a circle when

  1. all values of $K$ are integral
  2. $0 < K < 1$
  3. $K < 0$
  4. For one values of $K$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A = $(0,0)$ , B$(0,1)$ , C$(2k,3k)$ , D$(1,0)$

As we can see

$AD \perp AB$

$\angle A = 90$

$\angle C = 90$

$\implies m _{BC} \times m _{DC} = -1$

$\dfrac{3k - 1}{2k} \times {3k}{2k - 1} = -1$

$\implies k(9k - 3) = -(4k - 2)k$

$k = 0 , 9k + 4k = 2+ 3 \implies 13k = 5 \implies k = \dfrac{5}{13}$

But if $k = 0$, C will be $(0,0)$ which is A

$k = \dfrac{5}{13} $ only one point.