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#### Page No 8.6:

#### Question 1:

Plot the following points on the graph paper:

(i) (2,5)

(ii) (4, −3)

(iii) (−5, −7)

(iv) (7, −4)

(v) (−3, 2)

(vi) (7, 0)

(vii) (−4, 0)

(viii) (0, 7)

(ix) (0, −4)

(x) (0, 0)

#### Answer:

The following points are given below.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Letand be the coordinate axes.

(i) Here for the given point the abscissa is 2 units and ordinate is 5 units.

The point is in the first quadrant. So it will look like as shown in the following figure.

(ii) Here for the given point the abscissa is 4 units and ordinate is -3 units.

The point is in the fourth quadrant. So it will look like as shown in the following figure.

(iii) Here for the given point the abscissa is -5 units and ordinate is -7 units.

The point is in the third quadrant. So it will look like as shown in the following figure.

(iv) Here for the given point the abscissa is 7 units and ordinate is -4 units.

The point is in the fourth quadrant. So it will look like as shown in the following figure.

(v) Here for the given point the abscissa is -3 units and ordinate is 2 units.

The point is in the second quadrant. So it will look like as shown in the following figure.

(vi) Here for the given point the abscissa is 7 units and ordinate is 0 units.

The point is on the *x*-axis. So it will look like as shown in the following figure.

(vii) Here for the given point the abscissa is -4 units and ordinate is 0 units.

The point is on the *x*-axis. So it will look like as shown in the following figure.

(viii) Here for the given point the abscissa is 0 units and ordinate is 7 units.

The point is on the *y*-axis. So it will look like as shown in the following figure.

(ix) Here for the given point the abscissa is 0 units and ordinate is -4 units.

The point is on the *y*-axis. So it will look like as shown in the following figure.

(x) Here for the given point the abscissa is 0 units and ordinate is 0 units.

The point is basically intersection of the coordinate axes. So it will look like as shown in the following figure.

#### Page No 8.6:

#### Question 2:

Write the coordinates of each of the following points marked in the graph paper:

#### Answer:

The following graph is given in the question with the marked points and we are asked to write down their coordinates.

The distance of point A from *y-*axis is 3 units and that of from *x*-axis is 1 units. Since A lies in the first quadrant, so its coordinates are.

The distance of point B from *y-*axis is 6 units and that of from *x*-axis is 0 units. Since B lies on *x*-axis, so its coordinates are.

The distance of point C from *y-*axis is 0 units and that of from *x*-axis is 6 units. Since C lies on *y*-axis, so its coordinates are.

The distance of point D from *y-*axis is -3 units and that of from *x*-axis is 0 units. Since D lies on *x*-axis, so its coordinates are.

The distance of point E from *y-*axis is -4 units and that of from *x*-axis is 3 units. Since E lies in the second quadrant, so its coordinates are.

The distance of point F from *y-*axis is -2 units and that of from *x*-axis is -4 units. Since F lies in the third quadrant, so its coordinates are.

The distance of point G from *y-*axis is 0 units and that of from *x*-axis is -5 units. Since G lies on *y*-axis, so its coordinates are.

The distance of point H from *y-*axis is 3 units and that of from *x*-axis is -6 units. Since H lies in the fourth quadrant, so its coordinates are.

The distance of point P from *y-*axis is 7 units and that of from *x*-axis is -3 units. Since P lies in the fourth quadrant, so its coordinates are.

The distance of point Q from *y-*axis is 7 units and that of from *x*-axis is 6 units. Since Q lies in the first quadrant, so its coordinates are.

#### Page No 8.7:

#### Question 1:

Mark the correct alternative in each of the following:

The point of intersect of the coordinate axes is

(a) ordinate

(b) abscissa

(c) quadrant

(d) origin

#### Answer:

As we know that:

The distance of a point from *y*−axis is called its *x*−coordinate or abscissa.

The distance of a point from *x*−axis is called its *y−*coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

Example is shown in the graph

Thus the correct answer is (d).

#### Page No 8.7:

#### Question 2:

The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

#### Answer:

As we know that:

The distance of a point from *y*−axis is called its *x*−coordinate or abscissa.

The distance of a point from *x*−axis is called its *y−*coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

The origin is shown in the graph

Thus the correct answer is (a).

#### Page No 8.7:

#### Question 3:

The measure of the angle between the coordinate axes is

(a) 0°

(b) 90°

(c) 180°

(d) 360°

#### Answer:

As we know that *x−*axis and *y−*axis* *intersect to each other at point O and perpendicular to each other. So, the angle between the coordinate axes is.

Thus the correct answer is (b).

#### Page No 8.7:

#### Question 4:

A point whose abscissa and ordinate are 2 and −5 respectively, lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

#### Answer:

As shown in graph that a point whose abscissa and ordinate areand respectively lies in the fourth quadrant.

Thus the correct answer is (d).

#### Page No 8.7:

#### Question 5:

Points (−4, 0) and (7, 0) lie

(a) on x-axis

(b) y-axis

(c) in first quadrant

(d) In second quadrant

#### Answer:

Let the points P and Q whose coordinates are andrespectively. Locate the points and you will see that they lie on *x*-axis.

Thus the correct answer is (a).

#### Page No 8.7:

#### Question 6:

The ordinate of any point on x-axis is

(a) 0

(b) 1

(c) −1

(d) any number

#### Answer:

We know that the *y*−coordinates of every point on *x−*axis are zero. So, the coordinates of any point on the *x*−axis are of the form.

Thus the correct answer is (a).

#### Page No 8.7:

#### Question 7:

The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

#### Answer:

We know that the *x*−coordinate of every point on *y-*axis is zero. So, the coordinates of any point on the *x*−axis are of the form.

Thus the correct answer is (a).

#### Page No 8.7:

#### Question 8:

The abscissa of a point is positive in the

(a) First and Second quadrant

(b) Second and Third quadrant

(c) Third and Fourth quadrant

(d) Fourth and First quadrant

#### Answer:

The signs of coordinates of a point in various quadrants are shown in the following graph:

Thus the correct answer is (d).

#### Page No 8.7:

#### Question 9:

A point whose abscissa is −3 and ordinate 2 lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

#### Answer:

As we know that

In the first quadrant

In the second quadrant

In the third quadrant

In the fourth quadrant

The point whose abscissa is −3 which is negative and ordinate 2 is positive, so this point lies in the second quadrant.

Thus the correct answer is (b).

#### Page No 8.7:

#### Question 10:

Two points having same abscissae but different ordinate lie on

(a) x-axis

(b) y-axis

(c) a line parallel to y-axis

(d) a line parallel to x-axis

#### Answer:

Let the points and having the same abscissa but different ordinates be shown in the graph given below:

Fig: (location of two considered points)

And these points lie on a line parallel to *y−*axis

Thus the correct answer is (c).

#### Page No 8.7:

#### Question 11:

The perpendicular distance of the point *P* (4, 3) from *x*-axis is

(a) 4

(b) 3

(c) 5

(d) none of these

#### Answer:

The point is shown in the graph given below:

Thus the perpendicular distance of the point from *x*−axis is 3 units.

Thus the correct answer is (b).

#### Page No 8.7:

#### Question 12:

The perpendicular distance of the P (4,3) from y-axis is

(a) 4

(b) 3

(c) 5

(d) none of these

#### Answer:

The point is shown in the graph given below:

Thus the perpendicular distance of the point from *y−*axis is 4.

Thus the correct answer is (a).

#### Page No 8.7:

#### Question 13:

The distance of the point *P* (4, 3) from the origin is

(a) 4

(b) 3

(c) 5

(d) 7

#### Answer:

The point is shown in the graph given below:

In is right angled triangle where

By using Pythagoras theorem:

Thus the distance of the pointfrom the origin is 5.

Thus the correct answer is (c)

#### Page No 8.7:

#### Question 14:

The area of the triangle formed by the points *A*(2,0) *B*(6,0) and *C*(4,6) is

(a) 24 sq. units

(b) 12 sq. units

(c) 10 sq. units

(d) none of these

#### Answer:

Given that points A, Band Cform a triangle which is shown in the figure. We are asked to find the area of the triangle ΔABC.

Given that

Hence:

$AB=OB-OA\phantom{\rule{0ex}{0ex}}=6-2\phantom{\rule{0ex}{0ex}}=4$

CD = 6

By using formula,

$\u2206ABC=\frac{1}{2}\times AB\times CD\phantom{\rule{0ex}{0ex}}=\frac{1}{2}\times 4\times 6\phantom{\rule{0ex}{0ex}}=12squnits$

Thus the correct answer is (b).

#### Page No 8.7:

#### Question 15:

The area of the triangle formed by the points *P* (0, 1), *Q* (0, 5) and *R* (3, 4) is

(a) 16 sq. units

(b) 8 sq. units

(c) 4 sq. units

(d) 6 sq. units

#### Answer:

Given that the points,and form a triangle.

We are asked to find the area of the triangle ΔPQR which is shown in the figure.

Given that

Hence

By using formula,

Thus the correct answer is (d).

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