Tag: constructions

Questions Related to constructions

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

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

  1. Lies in the first quadrant

  2. Lies in the second quadrant

  3. Lies in third quadrat

  4. Cannot be found

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Correct Option: A

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

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

  1. 2

  2. 3

  3. -1

  4. -2

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Correct Option: A

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

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

  1. $(0,-4)$

  2. $(0,4)$

  3. $(-4,0)$

  4. $(0,0)$

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Correct Option: D
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 $OP=\left(\dfrac{0+0}{2},\dfrac{4+-4}{2}\right)$
$=\left(0,0\right)$

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

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

  1. $(6,6)$

  2. $(12,12)$

  3. $(2,2)$

  4. $(1,1)$

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Correct Option: A
Explanation:

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

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

The mid point of $(8,3)$ and $(4,9)$ is 

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

  1. $(6,6)$

  2. $(4,4)$

  3. $(9,9)$

  4. $(2,2)$

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Correct Option: A
Explanation:

The given points are $(8,3)$ and $(4,9)$

The mid point is given as$ \left(\dfrac {8+4}2,\dfrac {3+9}2\right)\(6,6)$

The mid point of $(-1,-3)$ and $(3,7)$

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

  1. (1, 2) 

  2. (0, 2) 

  3. (0, 4)

  4. (2 ,2)

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Correct Option: A
Explanation:

Given points $(-1,-3),(3,7)$

Mid point is given as $\left(\dfrac {-1+3}{2},\dfrac {-3+7}{2}\right)=(1,2)$

The mid point of $(4,9)  $ and $(8,3)$ is 

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

  1. $(6,6)$

  2. $(5,7)$

  3. $(-6,-6)$

  4. None.

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Correct Option: A
Explanation:

The mid point of $(4,9)  $ and $(8,3)$ is given as 

$\left(\dfrac{4+8}2,\dfrac{9+3}2\right)\\left(\dfrac {12}2,\dfrac{12}2\right)=(6,6)$

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

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

  1. $(5,6)$

  2. $(2,8)$

  3. $(5,7)$

  4. $(4,6)$

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Correct Option: A
Explanation:

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


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

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

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

  1. (2,1)

  2. (1,2)

  3. (2,-1)

  4. (1,-2)

Show answer
Correct Option: A
Explanation:

The points are $(3,4)$ and $(1,-2)$


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

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

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

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

  1. $a = b, b = -1$

  2. $a = 2, b = -3$

  3. $a = 3, b = - 2$

  4. $a =2, b = 3$

Show answer
Correct Option: D
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 $