Tag: divsion of line segmet in given ratio

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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

Find the points $A(a, b), B(-a, -b)$ and $P(a^2, ab)$ are collinear then the ratio in which p divides $\overline{AB}$ is 

  1. 1 + a : 1 - a

  2. 1 : a

  3. a : 1

  4. 1 - a : 1 + a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If P(a^2, ab) lies on AB, then (a^2 - a) / (-a - a^2) = ratio. (a(a-1)) / (-a(1+a)) = -(a-1)/(1+a) = (1-a)/(1+a).

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

In $\triangle ABC$ $PQR$ $\overline { BC } .\overline { CA } .\overline { AB } $ respectively dividing them in the ratio $1:4,3:2$ and $3:7$. The point $S$ divides $AB$ in the ratio $1:3$ Then $\dfrac { \left| \overline { AP } +\overline { BQ } +\overline { CR }  \right|  }{ \left| CS \right|  } =$

  1. $\dfrac {1}{5}$
  2. $\dfrac {2}{5}$
  3. $\dfrac {5}{2}$
  4. $\dfrac {7}{10}$
Reveal answer Fill a bubble to check yourself
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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

The ratio in which the line segment joining the points $\left(3,-4\right)$ and $\left(-5,6\right)$ is divided by the $x-$ axis, is

  1. $2:3$
  2. $3:2$
  3. $6:4$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The x-axis divides a line segment at a point where the y-coordinate is 0. Using the section formula, if the ratio is k:1, the y-coordinate is (k*6 + 1*(-4)) / (k+1) = 0, which gives 6k = 4, or k = 2/3.

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

The ratio in which the point $(x _{1} \sin^{2} \theta, y _{1} \cos^{2} \theta)$ divides the line joining $(x _{1}, 0)$ and $(0, y _{1})$ is -

  1. $\tan^{2} \theta : \cot^{2} \theta$
  2. $\cos \theta : \sin \theta $
  3. $\cos^{2} \theta : \sin^{2} \theta$
  4. $(1-\cos \theta) : (1-\sin \theta)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the section formula for a point (x, y) dividing (x1, 0) and (0, y1) in ratio m:n, we get x = n*x1 / (m+n) and y = m*y1 / (m+n). Setting x = x1*sin^2(theta) and y = y1*cos^2(theta) leads to the ratio m:n = tan^2(theta):cot^2(theta).