Tag: geometrical construction

Quizzes (3) Questions (18)

Questions Related to geometrical construction

Multiple choice 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

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the second 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 $Q$.

  1. $4$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 second step is $3$
Option $B$ is correct.

Multiple choice 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

There is a rectangular sheet of dimension $(2m-1)\times (2n-1)$, (where $m > 0, n > 0$). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length?

  1. $(m+n+1)^2$
  2. $mn(m+1)(n+1)$
  3. $4^{m+n-2}$
  4. $m^2n^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total no. of horizontal line=2m

Total no. of vertical lines=2n
($\because$ Each line is at unit distance and hence, total no. of lines=Distance/lenght +1).
To form a square from three lines,we must select one even and one odd numbered horizontal and vertical line.
$\therefore$ Ways possible of selecting such squares=$({ C } _{ 1 }^{ m }\times { C } _{ 1 }^{ m })\times ({ C } _{ 1 }^{ n }\times { C } _{ 1 }^{ n })$
$ ={ C } _{ 1 }^{ m }\times { C } _{ 1 }^{ m }\times { C } _{ 1 }^{ n }\times { C } _{ 1 }^{ n }$
$ ={ m }^{ 2 }\times { n }^{ 2 }$
$ ={ m }^{ 2 }{ n }^{ 2 }$

Multiple choice 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
The steps for constructing a perpendicular from point $A$ to line $PQ$ is given in jumbled order as follows: $(A$ does not lie on $PQ)$
1. Join $R-S$ passing through $A$.
2. Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.
3. From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S$.
4. Draw a line $PQ$ and take a point $A$ anywhere outside the line.
The second step in the process is:
  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 $PQ$ and take a point $A$ anywhere outside the line.

Step 2. Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.

Step 3. From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S.$

Step 4. Join $R−S$ passing through $A$.

So the second step is $2$.

Option $B$ is correct.

Multiple choice 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

To construct a perpendicular to a line($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the fourth 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 line.The point where these arcs intersect name that point as $Q$

  1. $4$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 line .The point where these arcs intersect name that as $Q$
Step 4. Draw line $PQ$
So the fourth step is $1$
Option $D$ is correct.

Multiple choice maths geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

$A B C$  is a triangle. The bisectors of the internal angle  $\angle B$  and external angle $\angle C$  intersect at  $D.$  if  $\angle B D C = 60 ^ { \circ }$  then  $\angle A$  is

  1. $120 ^ { \circ }$
  2. $180 ^ { \circ }$
  3. $60 ^ { \circ }$
  4. $150 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Consider $\triangle ABC$

Let $BC$ be extended to $E$
Since Angular bisectors Meet at $D$
$\angle ABD=\angle DBC\cdots(1)$
$\angle ACD=\angle DCE\cdots(2)$
Consider $ \triangle DBC$
By External sum property 
$\angle DCE=\angle BDC+\angle DBC$
$\implies 2\angle DCE=2(60^{\circ})+2\angle DBC$
$\implies \angle ACE=120^{\circ}+\angle ABC$
By external sum property of $\triangle ABC$
$\angle ACE=\angle BAC+\angle ABC$
$\implies \angle A=60^{\circ}$

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 geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

For drawing the perpendicular bisector of $PQ$, which of the following radii can be taken to draw arcs from $P$ and $Q$?

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

To draw a perpendicular bisector of a given side, take any length that is greater than half the length of the side. Draw the arcs from the edges of the base. The point where arcs meet is on the perpendicular bisector.


From the given options,

$\dfrac{2PQ}{3}$ can be considered to draw to draw arcs from edges $P, \ Q$

Remaining options has the value $\leq \dfrac{PQ}{2}$