Tag: constructions

Quizzes (6) Questions (134)

Questions Related to constructions

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

A point which divides the joint of $(1,2)$ and $(3,4)$ externally in the ratio $1:1$

  1. Lies in the first quadrant

  2. Lies in the second quadrant

  3. Lies in third quadrat

  4. Cannot be found
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The section formula for external division in the ratio m:n uses the formula ((mx2 - nx1)/(m - n), (my2 - ny1)/(m - n)). When the ratio is 1:1, the denominator becomes m - n = 1 - 1 = 0, which results in division by zero. Therefore, a point dividing a line segment externally in the ratio 1:1 cannot be found mathematically.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6: 1, then x equals

  1. 2

  2. 3

  3. -1

  4. -2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The y-axis divides a line segment in the ratio -x1:x2 or by setting the x-coordinate of the section formula to zero. Using the given coordinates (6, 4) and (x, -7) with a ratio of 6:1, the x-coordinate formula gives (6*x + 1*6)/(6 + 1) = 0, which yields 6x + 6 = 0, so x = -1.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

If $O(0,4)$ and $P(0,-4)$, are the co-ordinates of the line segment $OP$ then co-ordinate of its midpoint are

  1. $(0,-4)$
  2. $(0,4)$
  3. $(-4,0)$
  4. $(0,0)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Midpoint of a line segment having coordiantes $\left({x} _{1},{y} _{1}\right)$ and $\left({x} _{2},{y} _{2}\right)$ is $\left(\dfrac{{x} _{1}+{x} _{2}}{2},\dfrac{{y} _{1}+{y} _{2}}{2}\right)$

$\therefore $ Modpoint of $OP=\left(\dfrac{0+0}{2},\dfrac{4+-4}{2}\right)$
$=\left(0,0\right)$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Find the mid point of $(9,5)$ and $(3,7)$

  1. $(6,6)$
  2. $(12,12)$
  3. $(2,2)$
  4. $(1,1)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given points $(9,5),(3,7)$

Mid point is given as $\left(\dfrac{x _1+x _2}2,\dfrac{y _1,y _2}{2}\right)\\left(\dfrac{9+3}{2},\dfrac{5+7}{2}\right)\\left(\dfrac{12}{2},\dfrac{12}{2}\right)=(6,6)$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The mid point of $(2,3)$ and $(8,9)$ is 

  1. $(5,6)$
  2. $(2,8)$
  3. $(5,7)$
  4. $(4,6)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The points are $(x _1,y _1)=(2,3)$ and $(x _2,y _2)=(8,9)$


The mid point is given as $\left(\dfrac{2+8}2,\dfrac {3+9}2\right)$
                                
$\left(\dfrac {10}2,\dfrac {12}2\right)=(5,6)$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The mid point of $(3,4)$ and $(1,-2)$

  1. (2,1)

  2. (1,2)

  3. (2,-1)

  4. (1,-2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The points are $(3,4)$ and $(1,-2)$


The mid point of $(3,4)$ and $(1,-2)$ is given by 

$\left(\dfrac {x _1+x _2}2,\dfrac {y _1+y _2}2\right)\\\left(\dfrac{3+1}2,\dfrac {4-2}2\right)=(2,1)$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The mid-point of the line segment joining $( 2a, 4)$ and $(-2, 2b)$ is $(1, 2a + 1 )$. The values of $a$ and $b$ are 

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

Midpoint of two points $ =\left( \cfrac { { x } _{ 1 }+{ x} _{ 2 } }{ 2 } ,\cfrac { { y } _{ 1 }+y _{ 2 } }{ 2 }  \right) $
Given, midpoint of $ (2a,4) $ and $ (-2,2b) = (1,2a+1) $
$ => \left(\cfrac { 2a-2 }{ 2 } ,\cfrac { 4+2b }{ 2 }\right)= (1,2a+1) $
$ => \cfrac { 2a-2 }{ 2 } = 1 ; \cfrac { 4+2b }{ 2 } = 2a + 1 $
$ => 2a -2 = 2 $
$=> a = 2 $

And, $ \cfrac { 4+2b }{ 2 } = 2a + 1 $
$=> \cfrac { 4+2b }{ 2 } = 2(2) + 1 = 5 $
$ => 4 + 2b = 10 $
$ => 2b = 6 $
$=> b = 3 $