Nootan solutions for Mathematics [English] Class 9 ICSE 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, –1), (2, 2) and (3, 3)
2. (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

Draw the graph of the following line:

x + 3 = 0

Draw the graph of the following line:

2x – 7 = 0

Draw the graph of the following line:

y = 4

Draw the graph of the following line:

y + 6 = 0

Draw the graph of the following line:

3y + 5 = 0

Draw the graph of the following equation:

y = 2x

Draw the graph of the following equation:

x = 3y

Draw graph for equation given below: 

2x – 5y = 10

Draw graph for equation given below:

`1/2 x + 2/3 y = 5`

Draw graph for equation given below:

3x + 2y = 6

The graph of 3x + 2y = 12 meets the x-axis at point P and the y-axis at point Q. Use the graphical method, to find the co-ordinates of points P and Q.

Draw the graph of equation 3x – 4y = 12. Use the graph drawn to find:

1. y₁, the value of y, when x = 4.
2. y₂, the value of y, when x = 0.

Draw the graph of equation 5x + 4y = 20. Use the graph drawn to find:

1. x₁, the value of x, when y = 10.
2. y₁, the value of y, when x = 8.

Draw the graph of the equations x + y = 3, 2x – y = 3 and x + 2y = 4. Show that these three lines pass through the same point. Find the co-ordinates of this common point.

Draw the graph of the equations x + 2y = 3, 2x + y = 3 and x – y = 0. Show that these three lines pass through the same point. Find the co-ordinates of this common point.

Draw the graph of the pair of linear equations given below and then state whether the lines are parallel or perpendicular: 

2x + y = 5 and 2x + y = 7 

Draw the graph of the pair of linear equations given below and then state whether the lines are parallel or perpendicular:

x + 2y = 5 and 2x – y = 0

Draw the graph of the following equations and find their point of intersection.

x – 2y = 0 and 2x + 3y = 7

Draw the graph of y = x + 2 from x = –3 to x = 2.

Draw the graph of y = 2x – 1, y = 2x + 1 and y = 2x from x = 0 to x = 3. On the same graph paper and check whether these lines are parallel to each other.

Solve graphically:

x + y = 4, 3x + y = 6

Solve graphically:

x – 2y = 1, x + 2y = 5

Solve graphically:

x – y = 0, 2x + y = 6

Solve graphically:

x + 3y = –2, 2x – y = 3

Use graph paper and take 2 cm = 1 unit on both axes. Draw the graphs of x + y + 2 = 0 and 3x – 2y + 1 = 0. Write down the co-ordinates of the point of intersection of the lines.

Draw the graphs of the equations x + 2y = 4 and 3x – 2y = 4. Find the area of triangle formed by the lines and x-axis.

Draw the graphs of the equations x = –3, y = 2 and 2x + 3y = 6. Write down the vertices of the triangle formed by these lines.

A triangle is formed by the lines x + 2y – 3 = 0, 3x – 2y = –7 and y = –1. Find the area of this triangle.

Draw the graphs of the equations x – 5y + 14 = 0, 2x – y + 1 = 0 and x – 2y + 8 = 0. Write down the co-ordinates of the vertices of triangle formed.

Find the distance between the following points:

A(–6, 4) and B(2, –2)

Find the distance between the following points:

A(–5, –1) and B(0, 4)

Find the distance between the following points:

A(4, –1) and B(7, 3)

Find the distance between the following points:

A(3, 4) and B(5, 2)

Find the distance between the following points:

A(4, 5) and B(–2, 5)

Find the distance between the following points:

A(3, –4) and B(7, 0)

Find the distance of the following points from origin:

(3, –4)

Find the distance of the following points from origin:

(–8, –6)

Find the distance of the following points from origin:

(5, 12)

Find the distance of the following points from origin:

(7, 24)

Find the distance between the points (a, b) and (–b, a).

Find the distance between the points (2a, Зa) and (6a, 6а).

Find the distance between origin and the point (a, –b).

If the distance between the points (6, 0) and (0, y) is 10 units, find the value of y.

If the distance between the points (3, x) and (–2, –6) is 13 units, then find the value of x.

Prove that the distance between the origin and the point (–6, –8) is twice the distance between the points (4, 0) and (0, 3).

Find the co-ordinates of a point whose abscissa is 10 and its distance from the point (2, –3) is 10 units.

Prove that the following points are the vertices of a right-angled triangle:

A(–2, 2), B(13, 11) and C(10, 14)

Prove that the following points are the vertices of a right-angled triangle:

A(–1, –6), В(–9, –10) and C(–7, 6)

Prove that the following points are the vertices of an isosceles right-angled triangle: 

A(–8, –9), В(0, –3) and C(–6, 5)

Prove that the points A(1, 1), B(–1, –1) and `C(sqrt(3) - sqrt(3))` are the vertices of an equilateral triangle.

Prove that the points (–1, –2), (–2, –5), (–4, –6) and (–3, –3) are the vertices of a parallelogram.

Prove that the points (–4, –3), (–3, 2), (2, 3) and (1, –2) are the vertices of a rhombus.

Show that the following points are the vertices of a rectangle:

A(4, 2), В(0, –4), С(–3, –2), D(1, 4)

Show that the following points are the vertices of a rectangle:

A(1, –1), В(–2, 2), C(4, 8), D(7, 5)

Show that the points A(2, 1), B(0, 3), C(–2, 1) and D(0, –1) are the vertices of a square.

Show that the points (1, 1), (2, 3) and (5, 9) are collinear.

Show that the points (0, 0), (5, 3) and (10, 6) are collinear.

Show that the points (–3, 2), (2, –3) and `(1, 2sqrt(3))` lie on the circumference of that circle, whose centre is origin.

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

If (1, 1) and (1, 8) are the opposite vertices of a square, then find the co-ordinates of remaining two vertices.

The distance of the point (12, –5) from origin is ______.

Point (4, –3) lies in quadrant:

The distance of point (4, –6) from X-axis is ______.

The vertices of a triangle are (0, 0), (6, 0) and (0, 8). Its perimeter is ______.

If point (2, k) lies on the line 3x + 5y = 17, then the value of k is ______.

The distance between the points (3, 0) and (0, –3) is ______.

The pair of equations x = 3 and y = 4 graphically represent lines which are:

The distance between the points (4, 0) and (–4, 0) is ______.

The points (–3, 0), (3, 0) and (0, 4) are the vertices of:

Point (0, –3) lies:

Which of the following points lie on the graph of the equation 2x + y = 4?

Points (3, 1), (6, 4) and (8, 6) are: