Mathematics · Quantitative Aptitude

Coordinate Geometry and Construction

139 Questions

Coordinate geometry involves finding midpoints, calculating ratios of line segments, and understanding 3D projections. These concepts are crucial for tackling quantitative aptitude sections. Practice these questions to master geometric constructions and coordinate plotting.

Midpoint calculationsSection formulas3D geometry projectionsGeometric construction stepsLine segment ratios

Coordinate Geometry and Construction Questions

Multiple choice maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

The ratio at which the point $(5,4)$ divides the line $(3,2)$ and $(8,7)$

  1. $\dfrac 23$
  2. $\dfrac{-3}{2}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given points $(3,2);(8,7)$
Let the ratio be $m:n$
The dividing point is given as $\dfrac{8m+3n}{m+n}=5\\8m+3n=5m+5n\\3m=2n\\\dfrac mn=\dfrac 23$
Multiple choice maths geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3) Find the values of x and y

  1. 15, 6

  2. 33, 12

  3. 5, 0

  4. 14, 6

  5. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since line segment connecting $(x,6)$ and $(9,y)$ is bisected by the point $(7,3)$


Therefore, $\dfrac {x+9}2=7\Rightarrow x=5$ and $\dfrac {6+y}2=3\Rightarrow y=0$

$\therefore x=5, y=0$

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

With the help of a normal ruler and a compass only, which of the following line segment is possible to construct?

  1. $2.1\ cm$
  2. $4.2\ cm$
  3. $5.43\ cm$
  4. $3.3\ cm$
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
Explanation

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$.

So the lengths that can be measured are
$2.1\ \ cm,4.2\ \ cm$ and $3.3\ \ cm$
To measure $5.43$ we need a scale whose least count is $.001$

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

Which of the following line segments can be drawn with the help of a ruler and compass ?

  1. $1.234\ cm$
  2. $2.15\ cm$
  3. $2.5\ cm$
  4. $3.04\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So only $2.5 \ \ cm$ can be measured using a ruler and compass.
Hence 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

With the help of a normal ruler, which of the following line segment is possible to construct?

  1. $3.1\ cm$
  2. $4.234\ cm$
  3. $7.2\ cm$
  4. $1\ cm $
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Explanation

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So the lengths that can be measures are
$3.1\ \ cm$$,7.2\ \ cm$ and $1cm\ \ $
Options $A,C$ and $D$ are 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

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes last?

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

For constructing a line segment of given length steps are following:

Step 1 : Draw a line(2).
Step 2 :Take a point $A$ anywhere on the line(4).
Step 3 : Extend the compass by keeping one end on the $0 \ \ cm$ mark and other at given length on ruler(3).
Step 4 :  Draw an arc on the line by keeping the pointed end of the compass on the point $A$ .Mark the arc point as $B.$(1)
So $1.$ is the last step.
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

Construct a line segment of length $8.4\ cm$. Divide this line into $3$ equal parts and find the length of each part.

  1. $2.4\ cm$
  2. $4.2\ cm$
  3. $1.8\ cm$
  4. $2.8\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let length of each part $=x$

Lenght of three parts $=3x$
Given $3x=8.4$
$x=\dfrac{8.4}{3}=2.8$ 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

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes first?

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

Correct sequence is :

Step 1. Draw a line.
Step 2. Take a point $A$ anywhere on the line.
Step 3. Extend the compass by keeping one end on the $0 \ \ cm$ and other at the given length on the ruler.
Step 4. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc as point $B.$
So the first step is $2$
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

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes second?

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

Correct sequence is :

Step 1. Draw a line.
Step 2. Take a point $A$ anywhere on the line.
Step 3. Extend the compass by keeping one end on the $0 \ \ cm$ and other at the given length on the ruler.
Step 4. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc as point $B.$
So the second step is $4$
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

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes third?

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

Step 1 $:$ Draw a line .

Step 2 $:$ Take point $A$ anywhere on the line .
Step 3 $:$ Extend the compass by keeping one end on the $0\ \ cm$ mark at the given length of the rule.
Step 4 $:$ Draw an arc on the line by keeping the pointed end of the compass on the point $A$ .Mark the arc point as $B$
So $3$ is the third step .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

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 last.

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B 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 last step is $2$
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

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 $CD$.
Arrange them in correct order.

  1. $3,4,1,2$
  2. $1,2,3,4$
  3. $4,3,2,1$
  4. $3,1,2,4$
Reveal answer Fill a bubble to check yourself
A 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 sequence is $3,4,1,2$

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

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.