Answers posted by thanvigandhi_1

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Choose the correct answer from the given four options. The coordinates of the foot of perpendiculars from the point (2, 3) on the line $y = 3x + 4 $ is given by

answered Jul 6, 2014

Toolbox:Slope of a line is $ m = \large\frac{y_2-y_1}{x_2-x_1}$If two lines are perpendicular then t...

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Choose the correct answer from the given four options. The distance between the lines $ y = mx + c_1$ and $ y = mx + c_2$ is

answered Jul 3, 2014

Toolbox:Distance between parallel lines is $ d = \bigg| \large\frac{c_1-c_2}{\sqrt{A^2+B^2}} \bigg|$...

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Choose the correct answer from the given four options. The equations of the lines passing through the point (1, 0) and at a distance $ \large\frac{\sqrt 3 }{2}$ from the origin, are

answered Jul 3, 2014

Toolbox:Distance of a line $ax+by+c=0$ from the origin (0,0) is $d = \bigg| \large\frac{c}{\sqrt{A^2...

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Choose the correct answer from the given four options. The equations of the lines which pass through the point (3, –2) and are inclined at $ 60^{\circ}$ to the line $3 x + y = 1$ is

answered Jul 3, 2014

Toolbox:Equation of a line passing through a point $(x_1, y_1)$ and having slope $m$ is $ (y-y_1) = ...

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Choose the correct answer from the given four options. The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is

answered Jul 3, 2014

Toolbox:Distance of a point $(x_1,y_1)$ from the line $ax+by+c=0$ is $d=\bigg| \large\frac{ax_1+by_1...

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Choose the correct answer from the given four options. If the line $ \large\frac{x}{a}$$+ \large\frac{y}{b}$$=1$ passes through the points (2, –3) and (4, –5), then (a, b ) is

answered Jul 3, 2014

Toolbox:If a line $ax+by+c=0$ passes through a point $(x_1, y_1)$, then the coordinates can be subst...

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Choose the correct answer from the given four options. The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is

answered Jul 3, 2014

Toolbox:Slope of a line $'m' = -\large\frac{coefficient \: of \: x}{coefficient \: of \: y}$Angle b...

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Choose the correct answer from the given four options. The equation of the line passing through the point (1, 2) and perpendicular to the line $x+y+1 = 0 $ is

answered Jul 3, 2014

Toolbox:The slope of a line perpendicular to a given line where slope is $'m'$ is $ - \large\frac{1}...

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Choose the correct answer from the given four options. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is

answered Jul 3, 2014

Toolbox:If the slope of a line is $m$ then the slope of the line perpendicular to this is $ - \large...

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Choose the correct answer from the given four options. Slope of a line which cuts off intercepts of equal lengths on the axes is

answered Jul 3, 2014

Toolbox:Equation of a line in the intercept form is $ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$.Ste...

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Choose the correct answer from the given four options. A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x - axis is $ \large\frac{3}{5}$, its equation is

answered Jul 2, 2014

Toolbox:Equation of a line whose slope 'm' is given and intercept from the y - axis given is $y=mx+c...

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Choose the correct answer from the given four options. Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are

answered Jul 2, 2014

Toolbox:Equation of line whose join of points is $(x_1,y_1)$ and $(x_2, y_2)$ is $ \large\frac{y-y_1...

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Choose the correct answer from the given four options.Equation of the line passing through (1, 2) and parallel to the line y = 3x-1 is

answered Jul 2, 2014

Toolbox:Equation of a line having slope m and passing through $(x_1,y_1)$ is $ y-y_1=m(x-x_1)$If tw...

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Choose the correct answer from the given four options. If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be

answered Jul 2, 2014

Toolbox:The coordinates of the midpoint of the line joining the points $(x_1, y_1)$ and $(x_2, y_2)$...

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Find the equations of the lines through the point of intersection of the lines $x-y+1=0 $ and $ 2x-3y+5 = 0$ and whose distance from the point (3, 2) is $ \large\frac{7}{5}$

answered Jul 2, 2014

Toolbox:Equation of a line passing through the intersection of two lines is $a_1x+b_1y+c_1 + \lambda...

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Find the equation of the line which passes through the point (– 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point

answered Jul 1, 2014

Toolbox:Section formula : The coordinates of the point which divides the line joining the points $(x...

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A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point. \[\] [ Hint : $\large\frac{x}{a}$$ + \large\frac{y}{b}$$=1$ where $ \large\frac{1}{a}$$+\large\frac{1}{b}$ = constant = $ \large\frac{1}{k}$ (say ). This implies that $ \large\frac{k}{a}$$+\large\frac{k}{b}$$=1 \Rightarrow $ line passes through the fixed point (k, k).]

answered Jul 1, 2014

Toolbox:Equation of a line in its intercept form is $ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$Step...

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In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance $ \large\frac{\sqrt 6}{3}$ from the given point

answered Jul 1, 2014

Toolbox:Equation of a line passing through $(x_1, y_1)$ and making an angle $\theta $ is $ \large\fr...

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A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P \[\] [Hint: Let the slope of the line be $m$. Then the equation of the line passing through the fixed point $P (x_1 , y_1 )$ is $y - y_1 = m (x - x_1 )$. Taking the algebraic sum of perpendicular distances equal to zero, we get $ y - 1 = m (x - 1). $ Thus $(x_1 , y_1 ) $ is $(1, 1)$.]

answered Jul 1, 2014

Toolbox:Length of the perpendicular from $(x_1, y_1)$ to the line $ax+by+c=0$ is $ p = \bigg| \large...

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If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle \[\] [Hint: Find length of perpendicular (p) from (2, – 1) to the line and use $p = l \: \sin 60^{\circ}$, where $l$ is the length of side of the triangle]

answered Jul 1, 2014

Toolbox:Length of the perpendicular from $(x_1, y_1)$ to the line $ax+by+c=0$ is $ p = \bigg| \large...

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Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).

answered Jul 1, 2014

Toolbox:Slope of a line is $m = -\large\frac{coeff\: of \: x}{coeff\: of \: y}$$ \tan \theta = \bigg...

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Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of $120^{\circ}$ with the positive direction of $x$ - axis.\[\] [Hint: Use normal form, here $ \omega =30^{\circ}$.]

answered Jul 1, 2014

Toolbox:Equation of the line in the normal form is $ x \cos \omega + y \sin \omega = p$Step 1 :Given...

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If the intercept of a line between the coordinate axes is divided by the point (–5 4) in the ratio 1 : 2, then find the equation of the line.

answered Jul 1, 2014

Toolbox:Section formula : The coordinates of the point which divides the line joining the points $(x...

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For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.

answered Jul 1, 2014

Toolbox:If two lines are parallel then their slopes are equal.Distance of the perpendicular from a p...

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Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

answered Jul 1, 2014

Toolbox:If two lines are parallel, then their slopes are equal.Equation of a line passing through th...

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Find the equation of lines passing through (1, 2) and making angle $30^{\circ}$ with $y$ - axis.

answered Jul 1, 2014

Step 1 :It is given that the line makes an angle of $30^{\circ}$ with $y$ - axis.$ \therefore $ The ...

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Show that the tangent of an angle between the lines $ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$ and $ \large\frac{x}{a}$$-\large\frac{y}{b}$$=1$ is $ \large\frac{2ab}{a^2-b^2}$

answered Jun 30, 2014

Toolbox:Angle between two lines is $ \theta = \tan^{-1} \bigg| \large\frac{m_1-m_2}{1+m_1m_2} \bigg|...

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Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10

answered Jun 30, 2014

Toolbox:The distance from a point $(x_1, y_1)$ to a line $ax+by+c$ is $ \bigg| \large\frac{ax_1+by_1...

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Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.

answered Jun 30, 2014

Toolbox:Equation of a line which has $a$ and $b$ as the $x$ and $y$ intercepts is $ \large\frac{x}{a...

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Find the angle between the lines $y = (2 – \sqrt3 ) (x + 5)$ and $y = (2 + \sqrt3 ) (x – 7).$

answered Jun 30, 2014

Toolbox:Angle between two lines is $ \theta = \tan^{-1} \bigg| \large\frac{m_1-m_2}{1+m_1m_2} \bigg|...

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Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1)

answered Jun 30, 2014

Toolbox:Equation of a line pasing through two points $(x_1,y_1)$ and $(x_2, y_2)$ is $ \large\frac{y...

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Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes

answered Jun 30, 2014

Toolbox:Equation of a line which has $a$ and $b$ as the $x$ and $y$ intercepts is $ \large\frac{x}{a...

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Let A = {4, 6, 8, 10} and B = {3, 4, 5, 6, 7}. If f : A $ \rightarrow $ B is defined by f (x) = $ \large\frac{1}{2}$$x+1$ then represent f by a table

answered Jun 29, 2014

https://clay6.com/mpaimg/18iisc.jpg

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Let A = {4, 6, 8, 10} and B = {3, 4, 5, 6, 7}. If f : A $ \rightarrow $ B is defined by f (x) = $ \large\frac{1}{2}$$x+1$ then represent f by an arrow diagram

answered Jun 29, 2014

https://clay6.com/mpaimg/18isc.jpg

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Let A = {6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and f: A $ \rightarrow $ B be defined by f (x) = $ \large\frac{x-3}{3}$ represent f by a graph

answered Jun 29, 2014

https://clay6.com/mpaimg/17ivsc.jpg

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Let A = {6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and f: A $ \rightarrow $ B be defined by f (x) = $ \large\frac{x-3}{3}$ represent f by a table

answered Jun 29, 2014

https://clay6.com/mpaimg/17iiisc.jpg

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Let A = {6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and f: A $ \rightarrow $ B be defined by f (x) = $ \large\frac{x-3}{3}$ represent f by a set of ordered pairs

answered Jun 29, 2014

f = {(6, 1), (9, 2), (15, 14), (18, 5), (21, 6)}

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Let A = {6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and f: A $ \rightarrow $ B be defined by f (x) = $ \large\frac{x-3}{3}$ represent f by an arrow diagram.

answered Jun 29, 2014

https://clay6.com/mpaimg/17isc.jpg

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Represent the function f = {(–1, 2), (–3, 1),(–5, 6), (-4, 3) } as an arrow diagram

answered Jun 29, 2014

https://clay6.com/mpaimg/16iisc.jpg

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Represent the function f = {(–1, 2), (–3, 1),(–5, 6), (-4, 3) } as a table

answered Jun 29, 2014

https://clay6.com/mpaimg/16isc.jpg

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Let A = {5, 6, 7, 8 }; B = {–11, 4, 7, –10, –7, –9, –13 } and f = {(x, y); y = 3 – 2x, x $ \in $ A, y $ \in $ B } \[\] i) Write down the elements of f ii) What is the Co-domain \[\] iii) What is the range? iv) Identify the type of function.

answered Jun 29, 2014

(i) f = { (5, –7), (6, –9),(7, –11), (8, –13) } (ii) Co domain = {–11, 4, 7, –10, –7, –9, –13}

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Write the pre images of 2 and 3 in the function. f = {(12, 2), (13, 3), (15, 3), (14, 2), (17, 17)}

answered Jun 29, 2014

2 has two pre images 12 and 14 , 3 has two pre images 13 and 15

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For a given function F = {(1,3), (2,5), (4,7),(5,9),(3,1)} write the domain and range.

answered Jun 29, 2014

Domain = {1, 2, 3, 4, 5}, Range = {1, 3, 5, 7, 9}

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State whether each of the following diagrams define a function or not. Justify your answer.

answered Jun 29, 2014

Function

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State whether each of the following diagrams define a function or not. Justify your answer.

answered Jun 29, 2014

Not a function.

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Let \[|x| = \left\{ \begin{array}{l l} x, & \quad if\: x \geq 0 \\ -x, & \quad if\: x < 0 \end{array} \right.\] where x $ \in $ R \[\] Does the relation {(x, y) | y = |x|, x $ \in $ R} define a function? Find its range

answered Jun 29, 2014

Range will be the set of non-negative real numbers (either positive or zero).

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Which of the following relations are functions from A = {1, 4, 9, 16} to B = {–1, 2, –3, –4, 5, 6}? In case of a function, write down its range.\[\]( i) $f_1$ = {(1, –1), (4, 2), (9, –3), (16, –4)} (ii) $f_2$ = {(1, –4), (1, –1), (9, –3), (16, 2)} \[\] (iii) $f_3$ = {(4, 2), (1, 2), (9, 2), (16, 2)} (iv) $f_4$ = {(1, 2), (4, 5), (9, –4), (16, 5)}

answered Jun 29, 2014

(i) {–1, 2, –3, –4} (ii) $f_2$ is not a function (iii) {2} (iv) {2, 5, –4}

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Let X = {1, 2, 3, 4}. Examine whether each of the relations given below is a function from X to X or not. Explain. \[\] (i) f = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)} \[\] (ii) g = {(3, 1), (4, 2), (2, 1)} \[\] (iii) h = {(2, 1), (3, 4), (1, 4), (4, 3)}

answered Jun 29, 2014

(i) f is not a function (ii) g not a function (iii) h is a function.

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Does each of the following arrow diagrams represent a function? Explain.

answered Jun 29, 2014

Not a function.

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Does the following arrow diagram represent a function? Explain.

answered Jun 29, 2014

Its a function.

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