Tag: constructions

Quizzes (6) Questions (134)

Questions Related to constructions

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

The length of the median from the vertex A of a triangle whose vertices are $A (-1, 3),$ B $(1, -1)$ and C$(5,1)$ is 

  1. $5$
  2. $4$
  3. $1$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Length of the median from the vertex $A$ of a triangle $\triangle{ABC}$
Let $AD$ be the median.

$\Rightarrow\,D$ is the midpoint of $BC$

Using midpoint formula,$D=\left(\dfrac{1+5}{2},\,\dfrac{-1+1}{2}\right)=\left(3,\,0\right)$

Length of median $=AD=\sqrt{{\left(-1-3\right)}^2{}+{\left(0-3\right)}^{2}}=\sqrt{16+9}=\sqrt{25}=5$units.
Multiple choice maths constructions mid-point formula midpoints division of a line segment

The point on $X-axis$ equidistant from $(2,3)$and $(1,5)$ is

  1. $\left( \dfrac { -13 }{ 2 } ,0 \right) $
  2. $\left( \dfrac { 13 }{ 2 } ,0 \right) $
  3. $(13,0)$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the point be (x, 0). Equidistance means (x-2)^2 + (0-3)^2 = (x-1)^2 + (0-5)^2. Expanding: x^2 - 4x + 4 + 9 = x^2 - 2x + 1 + 25. Simplifying: -4x + 13 = -2x + 26, so -2x = 13, x = -13/2. The point is (-13/2, 0).

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

Let ${P} _{1}$ and ${P} _{2}$ be two fixed points in $xy-plane$. A line ${L} _{1}=0$ passes through ${P} _{1}$ intersects $y-axis$ at $B$ and the line ${L} _{2}=0$ passes through ${P} _{2}$ and intersects $x-axis$ at $A$. If ${L} _{1}=0$ and ${L} _{2}=0$ are perpendicular then the locus of mid-point of$AB$ is

  1. $Straight line$
  2. $Circle$
  3. $Ellipse$
  4. $Parabola$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The locus of the midpoint of a segment whose endpoints move on axes while the lines are perpendicular results in a straight line relationship based on the fixed points P1 and P2.

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

Let P be the point (1, 0) and Q a point on the curve ${ y }^{ 2 }=8x$. The locus of mid point of PQ is-

  1. ${ y }^{ 2 }-4x+2=0$
  2. ${ y }^{ 2 }+4x+2=0$
  3. ${ x }^{ 2 }+4y+2=0$
  4. ${ x }^{ 2 }-4y+2=0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=(1,0), Q=(h,k)$


$k^2=8h$


Let $(\alpha, \beta)$ be the mid-point of PQ.

$\alpha =\dfrac{h+1}{2}, \beta =\dfrac{k+0}{2}$

$2\alpha-1=h, 2\beta=k$

$(2\beta)^2=8(2\alpha-1)$

$\beta^2=4\alpha-2$

$\implies y^2-4x+2=0$