Title CORE Coordinate Geometry and Transformations English 3.4 MB 91
##### Document Text Contents
Page 1

UNIT-6

CLASS

X
CBSE-i

CORE

Coordinate
Geometry

and
Transformations

X

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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.

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(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 =

=

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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

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