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Quizzes (6) Questions (134)

Questions Related to constructions

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 point which divides the line segment joining $(-2, 4), (2, 7)$ in the ratio $2:1$ externally is

  1. $(6, 10)$
  2. $(2, \dfrac{10}{3})$
  3. $(\dfrac{-4}{3}, \dfrac{2}{3})$
  4. $( \dfrac{2}{3} ,6)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For external division in ratio m:n, the formula is (mx2 - nx1)/(m-n), (my2 - ny1)/(m-n). For (2,1) and points (-2,4), (2,7): x = (2*2 - 1*-2)/(2-1) = 6. y = (2*7 - 1*4)/(2-1) = 10.

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
A Correct answer
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

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at point P and Q respectively. Then the point O divides the segment PQ in the ratio

  1. 1:2

  2. 3:4

  3. 2:1

  4. 4:3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The parallel lines are 4x + 2y - 9 = 0 (or normalized as 2x + y - 4.5 = 0) and 2x + y + 6 = 0. A line through the origin has the form y = mx. It intersects the first line at P and the second line at Q. The distances from the origin to the lines along any ray are proportional to the constant terms of the parallel lines. Specifically, the ratio OP/OQ equals the ratio of the constant distances from the origin, which is 4.5 / 6 = 9/12 = 3/4.

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).