Equation of a Line Parallel to a Straight Line

Q. Draw the graphs of the following equations:

2x − 3y + 6 = 0
2x + 3y − 18 = 0
y − 2 = 0

Find the vertices of the triangle so obtained. Also, find the area of the triangle.

Q. Draw the graphs of x − y + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x-axis and shade the triangular area. Calculate the area bounded by these lines and x-axis.

Q. Two lines y=3x and x=3y intersects each other at

Q. draw the graph of 2x+y-6=0 and 2x-y=-2 also, find the area of the triangle formed by the above lines and x axis

Q. Prove that the diagonals of a rectangle ABCD with vertices A(2, −1), B(5, −1), C(5, 6) and D(2, 6) are
equal and bisect each other. [CBSE 2014]

Q.

Find the equation of the line parallel to the line $3x+2y=8$ and passing through the point $(0,1)$.

1. 2x+3y-2=0

2. 3x+2y-2=0

3. 3x+2y-3=0

4. 3x+2y+3=0

Q.

$ABCD$ is a convex quadrilateral. $3,4,5$ and $6$ points are marked on the sides $AB,BC,CD$ and $DA$ respectively. The no. of triangles with vertices on different sides are?

1. $270$

2. $220$

3. $282$

4. $342$

Q. What is value of y so that the line through (3, y) and (2, 7) is parallel to the line passing through (- 1 , 4) and (0, 6)?

1. 9
2. -8
3. 8
4. 9

Q. 29. If A(9, 9), (1, -3) are the end points of hypotenus of a right angled isosceles triangle, then the vertex is. A) (8, -2) B) (-8, 2) C) (8, -8) D) (0, 0)

Q.

Find the value of $x$ if the line passing through $(x,-3)$ and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

1. -2

2. 3

3. -3

4. 2

Q.

If the slopes of two lines are equal, then the lines are __ to each other.

Q.

From the given figure, find :

(i) the co-ordinates of A, B and C.

(ii) the equation of the line through A and parallel to BC.

Q.

(i) Find the equation of the line passing through (5, -3) and parallel to x - 3y = 4.

(ii) Find the equation of the line parallel to the line 3x + 2y = 8 and passing through the point (0, 1).

Q.

(i) Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x - 21y + 50 = 0 ?

(ii) Is the line x - 3y = 4 perpendicular to the line 3x - y = 7 ?

(iii) Is the line 3x + 2y = 5 parallel to the line x + 2y = 1 ?

(iv) Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.

Q.
Solve the following system of equations graphically and find the vertices and
area of the triangle formed by these lines and the y-axis.
$$\begin{gathered} 4x-y-4=0 \\ 3x+2y-14=0 \end{gathered}$$

Q.

A line passing through point ($\frac{1}{2},\frac{9}{4}$), has y-intercept of 3. Find the x-intercept of the line.

1. 0

2. 1

3. Not definite

4. Insufficient data

Q. Show graphically that the following given systems of equations is inconsistent i.e. has no solution:
$$\begin{gathered} x-2y=6 \\ 3x-6y=0 \end{gathered}$$

Q.

The intercepts made by a straight line on the -axis and -axis are –3 and 2 units respectively. Find:

i) the gradient of the line

ii) the equation of the line.

iii) the area of the triangle enclosed between the line and the co-ordinate axes.

1. 2/3, 3y-6=2x, 3 unit²

2. 2/3, 3y-6= x, 5 unit²

3. 3/2, 3y-4=2x, 8unit²

4. 1/3, 2y-6=2x, 3 unit²

Q.

The lines represented by 4x + 3y = 9 and px - 6y + 3 = 0 are parallel. Find the value of p.

Q.

Prove that the points (2, 3), (7, 5), (9, 8), (4, 6) are the vertices of a parallelogram.

Q. draw the graph of linear equation 3x+y=3, 3x+y=9

Q. Find the product of x-intercept and y-intercept of the line $2x+4y=10$.

1. 12.5

Q. In the figure, AB || CD and XY is the transversal.

Which of the following is incorrect?

1. $p={115}^{\circ }$
2. $q={115}^{\circ }$
3. $q={65}^{\circ }$
4. $r={115}^{\circ }$

Q.

Find the value of k, if the line represented by the equation 3x – ky = 12 passes through the point (4, 2). [2 MARKS]

Q.

ABCD is a rectangle whose sides AB has equation 3x-12y+5 =0. Find the slopes of the other sides of the rectangle

Q. the line segment joining P(-4, 5) and Q(3, 2) intersect the y- axis at R. PM and QN are perpendiculars from P and Q on the x axis.
find: 1) the ratio PR:QR
2) the cordinates of R
3) the area of the quadrilateral PMNQ

Q.

If 2y –$a^2$x = 3 and 2y – (4ax +1) = 0 are parallel, find the value of a, where a is a natural number.

Q.

Find the equation of the line through the intersection of 2x +y = 8, 3x – 7 = y and parallel to 4x +y = 11.

Q.

The perpendicular distance from the origin to a line is 7 and the perpendicular makes an angle of ${150}^{\circ }$ with the positive x-axis. Find the equation of the line.

1. 

2. 

3. 

4. 

Q. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

1. 
2. 
3. 
4.