Visualising Cartesian System in Two Dimensions

Q. Express y in terms of x in the equation 2x − 3y = 12. Find the points where the line represented by the equations 2x − 3y = 12 cuts the x-axis and y-axis.

Q.

The point (1, -4) lies in which quadrant?

1. I

2. IV

3. II

4. III

Q. Write the equation of a line passing through the point (3, 5) and parallel to x-axis.

Q.

Find the equation of a line whose slope = 0 and y-intercept = -5.

1. y = - x -5

2. y = x - 5

3. x = -5

4. y = - 5

Q.

Question 1
In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie?
Verify your answer by locating them on the Cartesian plane.

Q. In which quadrant does the following points lie?
(a) $(3,-8)$
(b) $(-1,-3)$
(c) $(2,5)$
(d) $(-7,3)$

Q. Write the equation of a line parallel to y-axis and passing through the point (−3, −7).

Q.

Choose the correct statement

1. Equation of AC is 2y = x

2. Equation of BD is y=3x-2

3. The point of intersection of the lines is ( 4, 2)

4. All the above

Q. Find the equation of a straight line with slope – 1/ 3 and y – intercept – 4.

1. 3y + x = -12
2. 3y + x = -12
3. 2y + x = 12
4. 3y + x = 12

Q. Solve the following system of linear equations graphically :

3x + y − 11 = 0, x − y − 1 = 0.
Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

Q.

The point $(-8,11)$ lies in the ____ quadrant.

Q.

For each of the equations given in select the equation whose graph can be made on a graph paper

(I) x+y=0 , y=2x , y=x , y=2x+1

Q. Write the equation of a line passing through the point (0, 4) and parallel to x-axis.

Q. Write the equations of the lines (i) PQ (ii) RS (iii) CD (iv) MN (v) XX (vi) YY'

figure

Q. If the slope and the y-intercept of a line are -2 and -3 respectively, which of the following is the equation of the line?

1. y = 2x + 3
2. y = -2x - 3
3. y = -3x - 2
4. y = 3x + 2

Q. Find the equation of a line whose slope = 0 and y-intercept = -5.

Q.

Q. $(-2,3)$ lies in the II quadrant.

1. True
2. False

Q. Which of the following is not a parallelogram?

1. Rhombus
2. Rectangle
3. Square
4. Trapezium

Q. At what angle do the diagonals of a rhombus bisect each other?

1. 180 degrees
2. 0 degrees
3. 90 degrees
4. 80 degrees

Q. Which quadrant(s) have points with a positive abscissa?

1. I, IV
2. I, II
3. IV only
4. I only

Q. find wheWrite the linear equation representing a line parallel to x axis and at a distance 4 units below x axis

Q. The y-intercept of the line plotted in the above graph is units.

1. 54
2. 64
3. 74

Q. Find the equation of the straight line which pass through (4, 3) and are respectively parallel and perpendicular to the x axis.

Q. In which quadrant does the point lie if $x$ co-ordinate is negative and $y$ co-ordinate is positive?

Q. In a parallelogram ABCD, if angle B = 60 degrees then what is the value of angle D?

1. 120 degrees
2. 40 degrees
3. 180 degrees
4. 60 degrees

Q. Two coordinates are enough to represent a point in 2 dimensional space.

1. True
2. False

Q. If PQRS is a rhombus and angle P = 70 degrees, then what is the value of angle PQR?

1. 35 degrees
2. 55 degrees
3. 45 degrees
4. 110 degrees

Q. write the y intercept of line that passes through 2, 2 and is perpendicular to line 3x+y=3