Nootan solutions for माठेमटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 19 - Co-ordinate Geometry: An Introduction [Latest edition]

Express the following equation in the form in which y is dependent variable.

3x + 4y = 15

Express the following equation in the form in which y is dependent variable.

6x – 5y = 7

Express the following equation in the form in which x is dependent variable.

4x – 3y = 8

Express the following equation in the form in which x is dependent variable.

3x + 7y = 12

Find the value of x and y if (3x, 5y) = (9, 10).

Find the value of x and y if (x + 3, 2y – 3) = (9, –9).

Find the value of x and y if (x + y, x – y) = (11, 3).

Find the value of x and y if (2x + y, x + 2y) = (5, 4).

Plot the following point on the cartesian plane:

(3, 2)

Plot the following point on the cartesian plane:

(–4, 3)

Plot the following point on the cartesian plane:

(–3, –4)

Plot the following point on the cartesian plane:

(4, –3)

Plot the following point on the cartesian plane:

(2, 0)

Plot the following point on the cartesian plane:

(–3, 0)

Plot the following point on the cartesian plane:

(0, 4)

Plot the following point on the cartesian plane:

(0, –3)

Plot the following point on the cartesian plane whose:

abscissa is 5 and ordinate is 2

Plot the following point on the cartesian plane whose:

abscissa is –2 and ordinate is 3

Plot the following point on the cartesian plane whose:

abscissa is 3 and ordinate is twice of the abscissa

Plot the following point on the cartesian plane whose:

ordinate is 8 and abscissa is three-fourth of ordinate

In the following, find the co-ordinates of the point whose abscissa is the solution of first equation and the ordinate is the solution of the second equation: 

5x – 1 = 9 and 3y + 1 = y – 5

In the following, find the co-ordinates of the point whose abscissa is the solution of first equation and the ordinate is the solution of the second equation:

`x + x/2 = 9/2` and 2y + (y – 3) = 9

In the following, find the co-ordinates of the point whose abscissa is the solution of first equation and the ordinate is the solution of the second equation:

3x – (1 – x) = 9 and `2y - 1 = 10 - (5y)/3`

In the following, find the co-ordinates of the point whose abscissa is the solution of first equation and the ordinate is the solution of the second equation:

`(13 - 3x)/2 = (x + 3)/3` and `(13 - 14y)/7 = (6 - 3y)/4`

From the following graph, find the co-ordinates of the point(s) satisfying the given condition.

1. the abscissa is 4
2. the ordinate is –4
3. the ordinate is 6
4. the abscissa is –3
5. the abscissa and ordinate are equal but opposite in sign.
6. the points whose abscissa are equal but ordinate are equal and opposite.

Plot the following points on the same graph paper and check whether they are collinear or not: 

(–1, –1), (2, 2) and (3, 3)

Plot the following points on the same graph paper and check whether they are collinear or not:

(1, 2), (0, 0) and (–1, –2)

In the following, three vertices of a rectangle are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex:

A(–1, 4), B(4, 4), C(4, –1)

In the following, three vertices of a rectangle are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex:

A(2, 0), B(2, 3), C(–4, 3)

In the following, three vertices of a rectangle are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex:

A(5, 2), B(5, 5), C(1, 5)

In the following, three vertices of a square ABCD are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex.

A(2, 1), B(2, 5), D(–2, 1)

In the following, three vertices of a square ABCD are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex. 

A(1, 1), В(1, 4), С(4, 4)

The three vertices of a parallelogram ABCD are A(–3, –4), B(2, –2) and C(2, 6). Plot these points on a graph paper and find the co-ordinates of the fourth vertex. Also find the area of the parallelogram.

Plot the points A(2, 1), B(2, –4), C(–3, –4) and D(–3, 1). What kind of quadrilateral is ABCD? Also find its area.

One vertex of a rectangle is at origin. Its two adjacent sides are along positive x-axis and along positive y-axis which are 4 units and 3 units respectively. Draw the rectangle on the graph paper and write the co-ordinates of its vertices.

Plot the point M(4, –3). Draw the perpendiculars MP and MQ from M to X-axis and Y-axis respectively. Write the co-ordinates of P and Q.

Draw the graph of the following line:

x = 2