##### Document Text Contents

Page 1

UNIT-6

CLASS

X

CBSE-i

CORE

Coordinate

Geometry

and

Transformations

X

Page 45

37

(i) Translation of a point P (x, y) to P’ (x + a , y + a)

x x + a

y y + a

Thus, point P(x, y) is a constant.

Similarly, Q (- - -3, 11)

=

=

From the above, we observe that:

Each point is translated to a distance of or 2 in the plane in a fixed direction.

In general, when x x + a, y y + a

i.e., P(x, y) P(x + a, y + a), then distance translated = = in a fixed

direction.

Here in this case, fixed direction is = = 1 i.e. m = tan450 or tan1350

Thus, direction is at an angle of 45o or 135o with x-axis.

Page 46

38

(i) Translation of a line segment PQ where P = P (x1, y1) and Q = Q (x2, y2).

Let each point (x, y) of line segment PQ is translated to (x + a, y + a).

So, P(x1, y1) 1 + a, y1 + a)

Q(x2, y2) 2 + a, y2 + a)

.

PQ =

=

=

Thus, the length of line segment obtained by translating a given line segment

through a given distance in a fixed direction always remains the same.

(ii) Translation of a ABC formed by the vertices A(x1, y1), B(x2, y2) and

C(x3, y3).

Let each point (x,y) is translation to (x + a, y + a).

Thus,

A( , ) +a, +a)

B( , ) +a, +a)

C( , ) +a, +a)

Now AB =

=

Page 90

82

SUGGESTED VIDEOS AND EXTRA READINGS:

Topic Web link

Important points

Coordinate geometry

http://mykhmsmathclass.blogspot.com/2009/11/important -

points-coordinate-geometry.html

To show given four

points are the

coordinates of vertices

of a rectangle

http://mykhmsmathclass.blogspot.com/2011/10/application -

of-distance-formula.html

In what ratio a given

point divides the join f

two given points?

http://mykhmsmathclass.blogspot.com/2011/10/application -

of-section-formula_26.html

Point of trisecton http://mykhmsmathclass.blogspot.com/2011/10/application -

of-section-formula.html

Area of triangle http://mykhmsmath class.blogspot.com/2011/10/area -of-

triangle -when-coordinates-of.html

Transformations-

Reflection

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -reflection.html

Transformations-

Reflection in a mirror

line

http://mykhmsmathclass.bl ogspot.com/2011/12/video -

transformations -reflection-along.html

Transformations-

Translation

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -translation.html

Transformations -

Rotation

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -rotation.html

http://mykhmsmathclass.blogspot.com/2009/11/important-points-coordinate-geometry.html

http://mykhmsmathclass.blogspot.com/2009/11/important-points-coordinate-geometry.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-distance-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-distance-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula_26.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula_26.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/area-of-triangle-when-coordinates-of.html

http://mykhmsmathclass.blogspot.com/2011/10/area-of-triangle-when-coordinates-of.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection-along.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection-along.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-translation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-translation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-rotation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-rotation.html

Page 91

Shiksha Kendra, 2, Community Centre, Preet Vihar,

Delhi-110 092 India

CENTRAL BOARD OF SECONDARY EDUCATION

UNIT-6

CLASS

X

CBSE-i

CORE

Coordinate

Geometry

and

Transformations

X

Page 45

37

(i) Translation of a point P (x, y) to P’ (x + a , y + a)

x x + a

y y + a

Thus, point P(x, y) is a constant.

Similarly, Q (- - -3, 11)

=

=

From the above, we observe that:

Each point is translated to a distance of or 2 in the plane in a fixed direction.

In general, when x x + a, y y + a

i.e., P(x, y) P(x + a, y + a), then distance translated = = in a fixed

direction.

Here in this case, fixed direction is = = 1 i.e. m = tan450 or tan1350

Thus, direction is at an angle of 45o or 135o with x-axis.

Page 46

38

(i) Translation of a line segment PQ where P = P (x1, y1) and Q = Q (x2, y2).

Let each point (x, y) of line segment PQ is translated to (x + a, y + a).

So, P(x1, y1) 1 + a, y1 + a)

Q(x2, y2) 2 + a, y2 + a)

.

PQ =

=

=

Thus, the length of line segment obtained by translating a given line segment

through a given distance in a fixed direction always remains the same.

(ii) Translation of a ABC formed by the vertices A(x1, y1), B(x2, y2) and

C(x3, y3).

Let each point (x,y) is translation to (x + a, y + a).

Thus,

A( , ) +a, +a)

B( , ) +a, +a)

C( , ) +a, +a)

Now AB =

=

Page 90

82

SUGGESTED VIDEOS AND EXTRA READINGS:

Topic Web link

Important points

Coordinate geometry

http://mykhmsmathclass.blogspot.com/2009/11/important -

points-coordinate-geometry.html

To show given four

points are the

coordinates of vertices

of a rectangle

http://mykhmsmathclass.blogspot.com/2011/10/application -

of-distance-formula.html

In what ratio a given

point divides the join f

two given points?

http://mykhmsmathclass.blogspot.com/2011/10/application -

of-section-formula_26.html

Point of trisecton http://mykhmsmathclass.blogspot.com/2011/10/application -

of-section-formula.html

Area of triangle http://mykhmsmath class.blogspot.com/2011/10/area -of-

triangle -when-coordinates-of.html

Transformations-

Reflection

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -reflection.html

Transformations-

Reflection in a mirror

line

http://mykhmsmathclass.bl ogspot.com/2011/12/video -

transformations -reflection-along.html

Transformations-

Translation

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -translation.html

Transformations -

Rotation

http://mykhmsmathclass.blogspot.com/2011/12/video -

transformations -rotation.html

http://mykhmsmathclass.blogspot.com/2009/11/important-points-coordinate-geometry.html

http://mykhmsmathclass.blogspot.com/2009/11/important-points-coordinate-geometry.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-distance-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-distance-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula_26.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula_26.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/application-of-section-formula.html

http://mykhmsmathclass.blogspot.com/2011/10/area-of-triangle-when-coordinates-of.html

http://mykhmsmathclass.blogspot.com/2011/10/area-of-triangle-when-coordinates-of.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection-along.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-reflection-along.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-translation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-translation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-rotation.html

http://mykhmsmathclass.blogspot.com/2011/12/video-transformations-rotation.html

Page 91

Shiksha Kendra, 2, Community Centre, Preet Vihar,

Delhi-110 092 India

CENTRAL BOARD OF SECONDARY EDUCATION