if the line 2x y k passes through the point which divides

If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then $$k$$ equals :

A. $$\frac{{29}}{5}$$

B. 5

C. 6

D. $$\frac{{11}}{5}$$

Answer : 6

Solution :
Let the joining points be $$A\left( {1,\,1} \right)$$ and $$B\left( {2,\,4} \right)$$
Let point $$C$$ divides line $$AB$$ in the ratio 3 : 2
So, by section formula we have
$$C = \left( {\frac{{3 \times 2 + 2 \times 1}}{{3 + 2}},\,\frac{{3 \times 4 + 2 \times 1}}{{3 + 2}}} \right) = \left( {\frac{8}{5},\,\frac{{14}}{5}} \right)$$
Since Line $$2x + y = k$$ passes through $$C\left( {\frac{8}{5},\,\frac{{14}}{5}} \right)$$
$$\therefore \,\,C$$ satisfies the equation $$2x + y=k$$
$$ \Rightarrow \frac{{2 + 8}}{5} + \frac{{14}}{5} = k\,\,\,\,\, \Rightarrow k = 6$$

Releted MCQ Question on
Geometry >> Straight Lines

Releted Question 1

The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

A. Collinear

B. Vertices of a parallelogram

C. Vertices of a rectangle

D. None of these

View Answer

Releted Question 2

The point (4, 1) undergoes the following three transformations successively.
(i) Reflection about the line $$y =x.$$
(ii) Translation through a distance 2 units along the positive direction of $$x$$-axis.
(iii) Rotation through an angle $$\frac{p}{4}$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.

A. $$\left( {\frac{1}{{\sqrt 2 }},\,\frac{7}{{\sqrt 2 }}} \right)$$

B. $$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$$

C. $$\left( { - \frac{1}{{\sqrt 2 }},\,\frac{7}{{\sqrt 2 }}} \right)$$

D. $$\left( {\sqrt 2 ,\,7\sqrt 2 } \right)$$

View Answer

Releted Question 3

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

A. isosceles

B. equilateral

C. right angled

D. none of these

View Answer

Releted Question 4

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

A. a straight line parallel to $$x$$-axis

B. a circle passing through the origin

C. a circle with the centre at the origin

D. a straight line parallel to $$y$$-axis

View Answer

If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then $$k$$ equals :

Releted MCQ Question on
Geometry >> Straight Lines

The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

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If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then $$k$$ equals :

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The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

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