Tag: constructions

Questions Related to constructions

If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.

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

  1. $3$

  2. $\dfrac{1}{2}$

  3. $2$

  4. $\dfrac{1}{4}$

Show answer
Correct Option: B
Explanation:

If $C$ is the midpoint of $AB$, then $C$ divides $AB$ in equal segments. Those segments are $AC$ and $AB$.

therefore, $AC=BC$. 
 $AC+BC=AB$ (As AC and BC are the segments of $AB$)
$\Rightarrow 2AC=2BC=AB\ \Rightarrow AC=BC=\dfrac{1}{2} AB$

Say true or false.
The mid-point of the line segment joining the points $P(x _1, y _1)$ and $Q(x _2, y _2)$ is 
$\dfrac {x _1+x _2}{2}, \dfrac {y _1+y _2}{2}.$
maths constructions mid-point formula midpoints division of a line segment

  1. True

  2. False

Show answer
Correct Option: A

If $O(0,0)$ and $P(-8,0)$ then co-ordinates of its midpoint are________.

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

  1. $(-4,0)$

  2. $(4,0)$

  3. $(0,-4)$

  4. $(0,0)$

Show answer
Correct Option: A
Explanation:

$O(0,0) $ and $P(-8,0)$ are given points.


The coordinates of the midpoint of 

$\overline{OP}=\left(\dfrac{x _1+x _2}{2},\dfrac{y _1+y _2}{2}\right)$

         $= \left( \dfrac {0-8}{2},\dfrac {0-0}{2}\right)$

         $=(-4,0)$

The mid point of line $AB$ with $A(2,3)$ and $B(5,6)$

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

  1. $(3.5,4.5)$

  2. $(3,4)$

  3. $(4,5)$

  4. None of these

Show answer
Correct Option: A
Explanation:

Given points $A(2,3)\equiv(x _1,y _1)$ and $B(5,6)\equiv(x _2,y _2)$


Mid points given as ,


$\Rightarrow\left(\dfrac{x _1+x _2}2,\dfrac{y _1+y _2}2\right)$

$\Rightarrow\left(\dfrac{2+5}2,\dfrac{3+6}2\right)$

$\Rightarrow\left(3.5,4.5\right)$

$(5,-2)$ is the middle line segment joining the parts $\left(\dfrac {x}{2},\dfrac {y+1}{2}\right)$ and $(x+1,y-3)$ then find the value of $x$ & $y$.

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

  1. True

  2. False

Show answer
Correct Option: A

Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are $(0.-1), (2, 1) and (0, 3)$

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

  1. $4$

  2. $8$

  3. $1$

  4. $2$

Show answer
Correct Option: B
Explanation:

$\\Area\>of\>triangle\>=4\times\>of\>triangle\>formed\>using\>mid-point\>\\=4\times(\frac{1}{2})[x-1(y _2-y _3)+x _2(y _3+y _1)+x _3(y _1-y _2)]\\=2[0+2(3-1)+0]=8sq\>unit$

What is the y intercept of the line that is parallel to $y=3x,$ and which bisects the area of rectangle with corners at $(0,0), (4,0) ,(4,2) $ and $(0,2)$? 

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

  1. $ -7$

  2. $-6$

  3. $ -5$

  4. $ -4$

Show answer
Correct Option: C
Explanation:

Rectangle's midpoints are $ = \left( {\frac{{0 + 4}}{2},\frac{{0 + 2}}{2}} \right) = \left( {\frac{4}{2},\frac{2}{2}} \right) = \left( {2,1} \right)$

Slope line y$=$ 3x will be :
${m _1} = 3$
Parallel line will be
${m _2} = 3$
Equation of line passing through (2 , 1)
$y - {y _1} = m(x - {x _1})$
$(y - 1) = 3(x - 2)$
$y - 1 = 3x - 6$
$y = 3x - 5$
Hence on comparing 
Y- intercept $=$ - 5

The mid-point of the line $(a, 2)$ and $(3, 6)$ is $(2, b)$. Find the numerical values of $a$ and $b$.

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

  1. $a=1$, $b=6$

  2. $a=2$, $b=4$

  3. $a=1$, $b=4$

  4. $a=2$, $b=6$

Show answer
Correct Option: C
Explanation:

Mid-point of $(a,2)$ and $(3,6)$ is $(2,b)$

=>$(2,b)=\left( \cfrac { a+3 }{ 2 } ,\cfrac { 2+6 }{ 2 }  \right) \ =>a=4-3,b=4\ =>a=1,b=4$

If $(3, -4)$ and $(-6, 5)$ are the extremities of a diagonal of a parallelogram and $(2, 1)$ is its third vertex, then its fourth vertex is?

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

  1. $(-1, 0)$

  2. $(-1, 1)$

  3. $(0, -1)$

  4. $(-5, 0)$

Show answer
Correct Option: D

If $(6, -3)$ is the one extremity of diameter to the circle $x^{2}+y^{2}-3x+8y-4=0$ then its other extremity is-

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

  1. $(3/2, -4)$

  2. $(-3, -5)$

  3. $(3, -5)$

  4. $(3, 5)$

Show answer
Correct Option: B