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#### Question 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)

The x co-ordinate of A(−3, 2) is negative and its y coordinate is positive. Therefore, point A(−3, 2) is in the second quadrant.

The x co-ordinate of B(−5, −2) is negative and its y coordinate is negative. Therefore, point B(−5, −2) is in the third quadrant.

The x co-ordinate of K(3.5, 1.5) is positive and its y coordinate is positive. Therefore, point K(3.5, 1.5) is in the first quadrant.

The x co-ordinate of D(2, 10) is positive and its y coordinate is positive. Therefore, point D(2, 10) is in the first quadrant.

The x co-ordinate of E(37, 35) is positive and its y coordinate is positive. Therefore, point E(37, 35) is in the first quadrant.

The x co-ordinate of F(15, −18) is positive and its y coordinate is negative. Therefore, point F(15, −18) is in the fourth quadrant.

The x co-ordinate of G(3, −7) is positive and its y coordinate is negative. Therefore, point G(3, −7) is in the fourth quadrant.

The x co-ordinate of H(0, −5) is zero. Therefore, point H(0, −5) is on the Y-axis.

The y co-ordinate of M(12, 0) is zero. Therefore, point M(12, 0) is on the X-axis.

The x co-ordinate of N(0, 9) is zero.  Therefore, point N(0, 9) is on the Y-axis.

The x co-ordinate of P(0, 2.5) is zero. Therefore, point P(0, 2.5) is on the Y-axis.

The x co-ordinate of Q(−7, −3) is negative and its y coordinate is negative. Therefore, point Q(−7, −3) is in the third quadrant.

#### Question 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) The x co-ordinate and y co-ordinate of a point are both positive in the first quadrant.

(ii) The x co-ordinate and y co-ordinate of a point are both negative in the third quadrant.

(iii) The x co-ordinate of a point is positive and y co-ordinate of a point is negative in the fourth quadrant.

(iv) The x co-ordinate of a point is negative and y co-ordinate of a point is positive in the second quadrant.

#### Question 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)

The given points are L(−2, 4), M(5, 6), N(−3, −4), P(2, −3), Q(6, −5), S(7, 0) and T(0, −5).
These point can be plotted on the co-ordinate system as follows:

#### Question 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 given points are A(3, 0), B(3, 3) and C(0, 3). These points can be plotted on the co-ordinate plane as follows:

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:

Write the equation of the line parallel to the Y-axis at a distance of 7 units from it to its left.

The equation of the line parallel to Y-axis at a distance of 7 units from it to its left is x = −7.

#### Question 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.

The equation of the line parallel to X-axis at a distance of 5 units from it and below the X-axis is y = −5.

#### Question 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 x co-ordinate of a point is its distance from the Y-axis and y co-ordinate is its distance from the X-axis.

The point of intersection of the line parallel to Y-axis at a distance 3 units from it to its left and the line parallel to X-axis at a distance 2 units below it is (−3, −2).

The equation of the line parallel to Y-axis at a distance 3 units from it to its left is x = −3.

#### Question 5:

X-axis and line x$-$4 are parallel lines. What is the distance between them?

Disclaimer: The question is incorrect. The question should be "Y-axis and line x = $-$4 are parallel lines. What is the distance between them? or X-axis and line y = $-$4 are parallel lines. What is the distance between them?"

If the question is "Y-axis and line x = $-$4 are parallel lines. What is the distance between them?" then the answer is as follows.

x = −4 is the equation of the line parallel to the Y-axis at a distance of 4 units and to the left of Y-axis.

Thus, the distance between them is 4 units.

OR

If the question is "X-axis and line y = $-$4 are parallel lines. What is the distance between them?" then the answer is as follows.

y = −4 is the equation of the line parallel to the X-axis at a distance of 4 units and below the X-axis.

Thus, the distance between them is 4 units.

#### Question 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) $-$2 = 0 (iii) x + 6 = 0 (iv) y = $-$5

(i)
x = 3 is the equation of the line parallel to Y-axis at a distance of 3 units and to the right of Y-axis.

Thus, the graph of the line x = 3 is parallel to Y-axis.

(ii)
y − 2 = 0

⇒ y = 2

y = 2 is the equation of the line parallel to X-axis at a distance of 2 units and above the X-axis.

Thus, the graph of the line y − 2 = 0 is parallel to X-axis.

(iii)
x + 6 = 0

⇒ x = −6

x = −6 is the equation of the line parallel to Y-axis at a distance of 6 units from it to its left.

Thus, the graph of the line x + 6 = 0 is parallel to Y-axis.

(iv)
y = −5 is the equation of the line parallel to X-axis at a distance of 5 units and below the X-axis.

Thus, the graph of the line y = −5 is parallel to X-axis.

#### Question 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 given points are A(2, 3), B(6, −1) and C(0, 5).

The line which includes these points is shown below:

It can be seen from the graph that the line intersects the X-axis at (5, 0) and the Y-axis at (0, 5).

#### Question 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
x = −4 is the equation of the line parallel to Y-axis at a distance of 4 units from it to its left.
y − 1 = 0 ⇒ y = 1
y = 1 is the equation of the line parallel to X-axis at a distance of 1 unit and above the X-axis.
2x + 3 = 0 ⇒ x = $-\frac{3}{2}$
x = $-\frac{3}{2}$ is the equation of the line parallel to Y-axis at a distance of $\frac{3}{2}$ units from it to its left.
3y − 15 = 0 ⇒ y = $\frac{15}{3}$ = 5
y = 5 is the equation of the line parallel to X-axis at a distance of 5 units and above the X-axis.

It can be seen from the figure that the co-ordinates of the points of intersection are , (−4, 5) and (−4, 1).

#### Question 9:

Draw the graphs of the equations given below

(i) x + y = 2 (ii) 3x $-$ y = 0 (iii) 2x + y = 1

(i)
The equation of the given line is xy = 2.

x + y = 2

⇒ y = 2 − x          .....(1)

Putting x = 0 in (1), we get

y = 2 − 0 = 2

Putting x = 2 in (1), we get

y = 2 − 2 = 0

Putting x = −1 in (1), we get

y = 2 − (−1) = 2 + 1 = 3

Putting x = 5 in (1), we get

y = 2 − 5 = −3

These values can be represented in the table in the form of ordered pairs as follows:

 x 0 2 −1 5 y 2 0 3 −3 (x, y) (0, 2) (2, 0) (−1, 3) (5, −3)

Plot these points on the graph paper.

The line is the graph of the equation x + = 2.

(ii)
The equation of the given line is 3x  y = 0.

3x  y = 0

⇒ y = 3x          .....(1)

Putting x = 0 in (1), we get

y = 3 × 0 = 0

Putting x = 1 in (1), we get

y = 3 × 1 = 3

Putting x = −1 in (1), we get

y = 3 × (−1) = −3

Putting x = 2 in (1), we get

y = 3 × 2 = 6

These values can be represented in the table in the form of ordered pairs as follows:

 x 0 1 −1 2 y 0 3 −3 6 (x, y) (0, 0) (3, 0) (−1, −3) (2, 6)

Plot these points on the graph paper.

The line is the graph of the equation 3x  y = 0.

(iii)
The equation of the given line is 2x + y = 1.

2x + y = 1

⇒ y = 1 − 2x          .....(1)

Putting x = 0 in (1), we get

y = 1 − 2 × 0 = 1 − 0 = 1

Putting x = 1 in (1), we get

y = 1 − 2 × 1 = 1 − 2 = −1

Putting x = −1 in (1), we get

y = 1 − 2 × (−1) = 1 + 2 = 3

Putting x = 2 in (1), we get

y = 1 − 2 × 2 = 1 − 4 = −3

These values can be represented in the table in the form of ordered pairs as follows:

 x 0 1 −1 2 y 1 −1 3 −3 (x, y) (0, 1) (1, −1) (−1, 3) (2, −3)

Plot these points on the graph paper.

The line is the graph of the equation 2x + y = 1.

#### 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 )

(ii) Any point on the line y = x is of the form .....
(A) ( a , a )      (B) ( o , a )        (C) ( a , o )      (D) ( a , $-$a )

(iii) What is the equation of the X-axis ?
(A) x = 0         (B) y = 0           (C) x + y = 0     (D) x = y

(iv) In which quadrant does the point ($-$4, $-$3) lie ?
(A) First (B) Second (C) Third (D) Fourth

(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

(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

(i)
The y co-ordinate of every point on the X-axis is 0. Thus, the co-ordinates of a point on the X-axis is (a, 0).

Hence, the correct answer is option (C).

(ii)
Putting xa in yx, we get

ya

Thus, any point on the line yx is of the form (aa).

Hence, the correct answer is option (A).

(iii)
The y co-ordinate of every point on the X-axis is 0. Therefore, the equation of the X-axis is y = 0.

Hence, the correct answer is option (B).

(iv)
The x co-ordinate of (−4, −3) is negative and its y co-ordinate is negative. Therefore, the point (−4, −3) lies in the third quadrant.

Hence, the correct answer is option (C).

(v)
The y co-ordinate of all the points (−5, 5), (6, 5), (−3, 5) and (0, 5) is 5. All these points lies on the line y = 5, which is parallel to the X-axis.

Thus, the line which includes the points (−5, 5), (6, 5), (−3, 5) and (0, 5) is parallel to the X-axis.

Hence, the correct answer is option (C).

(vi)
The point whose x co-ordinate is positive and y co-ordinate is negative lie in the fourth quadrant.

Thus, the points Q(3, −4) and R(1, −1) lie in the fourth quadrant.

Hence, the correct answer is option (B).

#### Question 2:

Some points are shown in the given 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 co-ordinate of a point is its distance from the Y-axis and y co-ordinate of a point is its distance from the X-axis.

The co-ordinates of point Q are (−2, 2) and the co-ordinates of point R are (4, −1).

(ii) The x co-ordinate of every point on the Y-axis is 0 and the y co-ordinate of every point on the X-axis is 0.

The co-ordinates of point T are (0, −1) and the co-ordinates of point M are (3, 0).

(iii) The point whose x co-ordinate is negative and y co-ordinate is negative lies in the third quadrant.

Thus, the point S(−3, −2) lies in the third quadrant.

(iv) The co-ordinates of point O are (0, 0).

Thus, O is the point whose x and y co-ordinates 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)

(i) The x co-ordinate of the point (5, −3) is positive and its y co-ordinate is negative. Therefore, the point (5, −3) lie in the fourth quadrant.

(ii) The x co-ordinate of the point (−7, −12) is negative and its y co-ordinate is negative. Therefore, the point (−7, −12) lie in the third quadrant.

(iii) The x co-ordinate of the point (−23, 4) is negative and its y co-ordinate is positive. Therefore, the point (−23, 4) lie in the second quadrant.

(iv) The x co-ordinate of the point (−9, 5) is negative and its y co-ordinate is positive. Therefore, the point (−9, 5) lie in the second quadrant.

(v) The x co-ordinate of the point (0, −3) is zero. Therefore, the point (0, −3) lie on the Y-axis.

(vi) The y co-ordinate of the point (−6, 0) is zero. Therefore, the point (−6, 0) lie on the 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)

The given points are A(1, 3),  B(−3, −1), C(1, −4), D(−2, 3), E(0, −8) and F(1, 0).

These points can be plotted on the co-ordinate system as follows:

#### Question 5:

In the graph alongside, line LM is parallel to the Y-axis.

(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) The line LM is parallel to the Y-axis and passing through the point (3, 0).

The equation of the line LM is x = 3 and at a distance of 3 units to the right of the Y-axis.

Thus, the distance of line LM from the Y-axis is 3 units.

(ii) The x co-ordinate of a point is its distance from the Y-axis and y co-ordinate is its distance from the X-axis.

Thus, the co-ordinates of the points P, Q and R are (3, 2), (3, −1) and (3, 0), respectively.

(iii)
x co-ordinate of point L = 3

x co-ordinate of point M = 3

∴ Difference between the x co-ordinates of the points L and M = 3 − 3 = 0

Thus, the difference between the x co-ordinates 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 equations of the lines parallel to X-axis and at a distance 5 units from it are y = 5 and y = −5.

Thus, there are two lines which are parallel to X-axis and having a distance 5 units from it.

#### Question 7:

If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a ?