Solutions- Practice Set and Problem Sets
Practice set 7.1 :
Question 1.1. State in which quadrant or on which axis do the following points lie.
A(-3, 2), B(-5, -2), K(3.5, 1.5), D(2, 10), E(37, 35), F(15, -18), G(3, -7), H(0, -5), M(12, 0), N(0, 9), P(0, 2.5), Q(-7, -3)
| Coordinates | Quadrant/axis |
| A(-3,2) | Quadrant II |
| B (-5,-2) | Quadrant III |
| K (3.5, 1.5) | Quadrant I |
| D (2, 10) | Quadrant I |
| E (37,35) | Quadrant I |
| F (15, -18) | Quadrant IV |
| G (3, -7) | Quadrant IV |
| H (0,-5) | Y-axis |
| M (12,0) | X-axis |
| N (0,9) | Y-axis |
| P (0, 2.5) | Y-axis |
| Q(-7,-3) | Quadrant III |
Question 1.2. In which quadrant are the following points ?
(i) whose both co-ordinates are positive.
(ii) whose both co-ordinates are negative.
(iii) whose x co-ordinate is positive, and the y co-ordinate is negative.
(iv) whose x co-ordinate is negative and y co-ordinate is positive.
(i) Quadrant I
(ii) Quadrant III
(iii) Quadrant IV
(iv) Quadrant II.
Question 1.3. Draw the co-ordinate system on a plane and plot the following points.
L(-2, 4), M(5, 6), N(-3, -4), P(2, -3), Q(6, -5), S(7, 0), T(0, -5)
Practice set 7.2 :
Question 2.1. On a graph paper plot the points A (3,0), B(3,3), C(0,3). Join A, B and B, C. What is the figure formed ?
The x co-ordinate of point is its distance from the Y-axis and y co-ordinate of point is its distance from the X-axis.
Here, OA = AB = BC = OC = 3 units
Therefore, the figure formed is a square.
Question 2.2. Write the equation of the line parallel to the Y-axis at a distance of 7 units from it to its left.
The line is 7 units to the left of the Y-axis.
- Left of the Y-axis means on the negative X-side.
- Therefore, x = −7.
Question 2.3. Write the equation of the line parallel to the X-axis at a distance of 5 units from it and below the X-axis.
A line parallel to the X-axis will also have an equation of the form y = k (where k is a constant).
The line is 5 units below the X-axis, which means it lies on the negative Y-side.
Hence, k = −5
Therefore, the equation of the required line is: y = -5
Question 2.4. The point Q( -3, -2) lies on a line parallel to the Y-axis. Write the equation of the line and draw its graph.
The point Q(- 3, - 2) lies on a line parallel to the Y-axis.
The point Q lies in quadrant III
The equation of a line parallel to the Y-axis is of the form x = a.
So the equation of this line is x = - 3.
The graph of this line is shown below :
Question 2.5. X-axis and line x = -4 are parallel lines. What is the distance between them?
Equation of Y-axis is x = 0.
Equation of the line parallel to the Y-axis is x =- 4.
∴ Distance between the Y-axis and the line x = - 4 is 0 - (- 4) = 0 + 4 = 4 units
∴ The distance between the Y-axis and the line x =- 4 is 4 units.
Question 2.6. Which of the equations given below have graphs parallel to the X-axis, and which ones have graphs parallel to the Y-axis ?
(i) x = 3 (ii) y - 2 = 0 (iii) x + 6 = 0 (iv) y = -5
The equation of a line parallel to the X-axis is of the form y = b.
(ii) y - 2 = 0 i.e. y = 2 and (iv) y = - 5
The graphs of these two lines are parallel to the X-axis.
The equation of a line parallel to the Y-axis is of the form x = a.
(i) x = 3 and (iii) x + 6 = 0 i.e. x =- 6.
The graphs of these two lines are parallel to the Y-axis.
Question 2.7. On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If those points are collinear then draw the line which includes them. Write the co-ordinates of the points at which the line intersects the X-axis and the Y-axis.
The points are collinear.
The line intersects the X-axis in the point Q(5, 0) and the Y-axis in the point C(0, 5).
Question 2.8. Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection.
x + 4 = 0, y - 1 = 0, 2x + 3 = 0, 3y - 15 = 0
X + 4 = 0 ∴ x = -4. This line is parallel to the Y-axis and to its left at a distance of 4 units.
y - 1 = 0 ∴ y = 1. This line is parallel to the X-axis and above it at a distance of 1 unit.
2x + 3 = 0 ∴ 2x = -3 ∴ x = -3/2 ∴ x = -1.5
This line is parallel to the Y-axis and to its left at a distance of 1.5 units.
3y – 15 = 0 ∴ 3y = 15 ∴ y = 15/3 ∴ y = 5
This line is parallel to the X-axis and above it at a distance of 5 units.
The coordinates of the points of intersection of the lines
(i) x + 4 = 0 and y – 1 = 0 are (-4, 1).
(ii) x + 4 = 0 and 3y – 15 = 0 are (-4, 5).
(iii) 2x + 3 = 0 and y-1 = 0 are (-1.5, 1).
(iv) 2x + 3 = 0 and 3y - 15 = 0 are (-1.5, 5).
Question 2.9. Draw the graphs of the equations given below
(i) x + y = 2 (ii) 3x - y = 0 (iii) 2x + y = 1
First, we find four solutions for each of the equations and make tables
(i) x + y = 2
| x | -1 | 0 | 1 | 2 |
| y | 3 | 2 | 1 | 0 |
| (x, y) | (-1,3) | (0, 2) | (1,1) | (2, 0) |
(ii) 3x - y = 0
| x | -1 | 0 | 1 | 2 |
| y | -3 | 0 | 3 | 6 |
| (x, y) | (-1, -3) | (0, 0) | (1, 3) | (2, 6) |
(iii) 2x + y = 1
| x | -1 | 0 | 1 | 2 |
| y | 3 | 1 | -1 | -3 |
| (x, y) | (-1, 3) | (0, 1) | (1, -1) | (2, -3) |
Problem set 7 :
Question 1. Choose the correct alternative answer for the following quesitons.
(i) What is the form of co-ordinates of a point on the X-axis ?
(A) (b, b) (B) (o, b) (C) (a, o) (D) (a, a)
(C) (a, o)
(ii) Any point on the line y = x is of the form .....
(A) (a, a) (B) (o, a) (C) (a, o) (D) (a, - a)
(A) (a, a)
(iii) What is the equation of the X-axis ?
(A) x = 0 (B) y = 0 (C) x + y = 0 (D) x = y
(B) y = 0
(iv) In which quadrant does the point (-4, -3) lie ?
(A) First (B) Second (C) Third (D) Fourth
(C) Third
(v) What is the nature of the line which includes the points (-5,5), (6,5), (-3,5), (0,5) ?
(A) Passes through the origin, (B) Parallel to Y-axis.
(C) Parallel to X-axis (D) None of these
(C) Parallel to X-axis
(vi) Which of the points P (-1,1), Q (3,-4), R(1,-1), S (-2,-3), T (-4,4) lie in the fourth quadrant ?
(A) P and T (B) Q and R (C) only S (D) P and R
(B) Q and R
Question 2. Some points are shown in the figure.
With the help of it answer the following questions :
(i) Write the co-ordinates of the points Q and R.
(ii) Write the co-ordinates of the points T and M.
(iii) Which point lies in the third quadrant ?
(iv) Which are the points whose x and y co-ordinates are equal ?
(i) The coordinates of the points Q and R are (- 2, 2) and (4, - 1) respectively.
(ii) The coordinates of the points T and M are (0, - 1) and (3, 0) respectively.
(iii) The point S lies in the third quadrant.
(iv) x and y coordinates of the point O (origin) are equal.
Question 3. Without plotting the points on a graph, state in which quadrant or on which axis do the following point lie.
(i) (5, -3) (ii) (-7, -12) (iii) (-23, 4) (iv) (-9, 5) (v) (0, -3) (vi) (-6, 0)
| Coordinates | Quadrant/Axis |
| (i) (5, -3) | Quadrant IV |
| (ii) (-7, - 12) | Quadrant III |
| (iii) ( - 23, 4) | Quadrant II |
| (iv) (- 9, 5) | Quadrant II |
| (v) (0, -3) | Y-axis |
| (vi) (- 6, 0) | X-axis |
Question 4. Plot the following points on the one and the same co-ordinate system.
A(1, 3), B(-3, -1), C(1, -4), D(-2, 3), E(0, -8), F(1, 0)
Question 5. In the graph alongside, line LM is parallel to the Y-axis. (Fig.)
(i) What is the distance of line LM from the Y-axis ?
(ii) Write the co-ordinates of the points P, Q and R.
(iii) What is the difference between the x co-ordinates of the points L and M?
(i) Line LM is perpendicular to the X-axis at the point (3, 0).
The equation of Y-axis is x = 0.3 > 0.
∴ the distance of line LM from the Y-axis = 3 – 0 = 3.
(ii) The coordinates of the points P, Q and R are (3, 2), (3, - 1) and (3, 0) respectively.
(iii) The coordinates of the point L are (3, 3) and those of point M are (3, - 3).
Their x-coordinates are the same, which is 3. 3 – 3 = 0.
∴ the difference between the x-coordinates of the points L and M is 0.
Question 6. How many lines are there which are parallel to X-axis and having a distance 5 units?
The equation of a line parallel to the X-axis is of the form y = b. Here, the distance given is 5 units.
∴ y = 5 and y = - 5 are two lines which are parallel to the X-axis.
Question 7. If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a ?
a is a real number. If a < 0, then x = - a is a line parallel to the Y-axis and to its left.
If a > 0, then x = a is a line parallel to the Y-axis and to its right. The distance between the Y-axis and the line x = a is a - 0 = a.
∴ the distance between the Y-axis and the line x = a is | a |.