Tag: basics of a straight line

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Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If the straight line through the point $P(3,4)$ makes an angle $\cfrac{\pi}{6}$ with the x-axis and meets the line $3x+5y+1=0$ at $Q$, the length $PQ$ is

  1. $\dfrac {132}{12\sqrt {3}+5}$
  2. $\dfrac {132}{12\sqrt {3}-5}$
  3. $\dfrac {132}{5\sqrt {3}+12}$
  4. $\dfrac {132}{5\sqrt {3}-12}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The equation of straight line passing through $P(3,4)$ is $y=\tan \dfrac{\pi}{6}{x}+(4-3\tan \dfrac{\pi}{6})\implies y=\dfrac{x}{\sqrt{3}}+4-\sqrt{3}$

The point of intersection will be $\bigg(\dfrac{55-57\sqrt{3}}{5+3\sqrt{3}},\dfrac{-10+3\sqrt{3}}{5+3\sqrt{3}}\bigg)$
Length will be $30(5-3\sqrt{3})$

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If $m$ and $b$ are real numbers and $mb > 0$, then the line whose equation is $y = mx + b$ cannot contain the point-

  1. $(0, 2009)$
  2. $(2009, 0)$
  3. $(0, -2009)$
  4. $(20, -100)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$y= mx + b$
for (2009,0)
substituting in the given line
we get $2009m+b=0$
that is possible only if $mb < 0$
which contradicts our initial assumption mb > 0
so option is $b$
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The graph of $\dfrac {7x}{2}=18+\dfrac {4}{5}x-45$ is line____

  1. Parallel to $x-$axis at a distance of $10$ units from the origin
  2. Parallel to $y-$axis at a distance of $10$ units from the origin
  3. Parallel to $x-$axis at a distance of $20$ units from the origin
  4. Parallel to $y-$axis at a distance of $20$ units from the origin

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cfrac { 7x }{ 2 } =18+\cfrac { 4 }{ 5 } x-45\ \Rightarrow \cfrac { 7x }{ 2 } -\cfrac { 4x }{ 5 } =-27\ \Rightarrow \cfrac { 35x-8x }{ 10 } =-27\ \cfrac { 27x }{ 10 } =-27\ \Rightarrow x=-10$

Therefore graph is a straight line parallel to y-axis at a distance of $10$ units from the origin.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The equation  of a line is given by $3x - 2y = 9$ has how many possible solution?

  1. One solution

  2. No solution

  3. Two solution

  4. Infinitely many solution
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A linear equation in two variables represents a line in the coordinate plane. A line contains infinitely many points, and each point on the line is a valid solution to the equation. Therefore, the equation 3x - 2y = 9 has infinitely many solutions, not just one, two, or none.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The number of triangles that the four lines $y=x+3$, $y=2x+3$, $y=3x+2$, and $y+x=3$ form is?

  1. $4$
  2. $2$
  3. $3$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The given lines are $y=x+3, y=2x+3, y=3x+2$ Vand $y+x=3$ and $y+x=3$

Slopes of these lines are different from each other 
So, combinations of $3$ lines form a triangle 
$\therefore$ Number of triangles formed $=\, ^4C _3$
                                                   $=4$

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If sum of distance of a point from two perpendicular lines in a plane is $1$, then its locus is ?

  1. Square

  2. Circle

  3. A straight line

  4. An intersecting line
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x axis & y axis are the perpendicular lines. The sum of the distances from point $p(x, y)$ is $1$ 

i.e.,$|x| + |y| = 1$

The locus of the point 'p' which is the rhombus whose sides are $x + y = 1 ; -x + y = 1 ; x - y = 1 ; -x - y = 1$

$\bot r$ lines other than coordinate axis gives same result so locus is a square.