Tag: constructions

Quizzes (6) Questions (134)

Questions Related to constructions

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

The co -ordinates of the midpoint of a line segment joining $ p(5,7) $ and $ Q (-3,3) $ are........

  1. $ (2,4) $
  2. $ (1,5 ) $
  3. $ (4,2 ) $
  4. $ (2,5 ) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given,

$P(5,7),Q(-3,3)$

mid point is given by,

$(x,y)=\left ( \dfrac{5-3}{2},\dfrac{7+3}{2} \right )$

$\Rightarrow (x,y)=(1,5)$
Multiple choice maths constructions mid-point formula midpoints division of a line segment

The locus of the mid point of the portion intercepted between the axes by the line $x{\,}cos\alpha+y{\,}sin{\,} \alpha=p$, where $p\inR$, is

  1. $x^2+y^2=\dfrac{4}{p^2}$
  2. $\dfrac{1}{x^2}+\dfrac{1}{y^2}=\dfrac{4}{p^2}$
  3. $\dfrac{1}{x^2}-\dfrac{1}{y^2}=\dfrac{4}{p^2}$
  4. $\dfrac{1}{x^2}+\dfrac{1}{y^2}=\dfrac{2}{p^2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths constructions mid-point formula midpoints division of a line segment

I every points on the line $(a _{1}-a _{2})x+(b _{1}-b _{2}),y=c$ is equidistance from the points $(a _{1},b _{1})$  and $(a _{2},b _{2})$ then $2c=$  

  1. $a _{1}^{2}-b _{1}^{2}+a _{2}^{2}-b _{2}^{2}$
  2. $a _{1}^{2}+b _{1}^{2}+a _{2}^{2}+b _{2}^{2}$
  3. $a _{1}^{2}+b _{1}^{2}-a _{2}^{2}-b _{2}^{2}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice maths constructions mid-point formula midpoints division of a line segment

The midpoint of the interval in which $x^{2}-2(\sqrt{-x})^{2}-3<0$ is satisfied, is

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

The expression sqrt(-x)^2 is defined for x <= 0 and equals -x. The inequality is x^2 - 2(-x) - 3 < 0 => x^2 + 2x - 3 < 0 => (x+3)(x-1) < 0. Since x <= 0, the interval is [-3, 0]. The midpoint is (-3+0)/2 = -3/2.

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

A tangent to the circle $x^{2}+y^{2}=a^{2}$ meets the axes at points A and B. The locus of the mid point of AB is 

  1. $\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{1}{a^{2}}$
  2. $\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{4}{a^{2}}$
  3. $\frac{1}{x^{2}}+\frac{1}{y^{2}}=4a^{2}$
  4. $\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{a^{2}}{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer