Preparation For Dilatation

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Preparation for Dilatation is the transformation of the given figure according to the scale factor. The size of the image is greater than the actual image if the scale factor is greater than one and the size of the image is smaller than the actual image if the scale factor is smaller than one. The size of the image is as it is if the scale factor is 0.

Example 1 – Preparation for Dilatation:

Find out the dilatation for the following figure with the scale factor 2.

Dilatation 1

Solution:

Given the vertexes of the given figure is A (6, 5), B (4, 3) and C (7, 1).

The given scale factor is 2 so the dilatation of the given figure will be larger than actual figure.

So now multiply the x – coordinates and y – coordinates by 2.

A’ (6*2, 5*2), B’ (4*2, 3*2) and C’ (7*2, 1*2)

A’ (12, 10), B’ (8, 6) and C’ (14, 2).

Now plot these points in a graph and join all the vertices A’B’C’.

Dilatation

Triangle A’B’C’ is the dilatation of Triangle ABC with the scale factor 2.

Example 2 – Preparation for Dilatation:

Find ...
... out the dilatation for the following figure with the scale factor 0.5.

Dilatation 2

Solution:

Given the vertexes of the given figure is A (6, 6), B (9, 6), C (6, 3) and D (9, 3)

The given scale factor is 0.5 so the dilatation of the given figure will be larger than actual figure.

So now multiply the x – coordinates and y – coordinates by 0.5.

A’ (6*0.5, 6*0.5), B’ (9*0.5, 6*0.5), C’ (6*0.5, 3*0.5) and D’ (9*0.5, 3*0.5)

A’ (3,3), B’ (4.5, 3), C’ (3, 1.5) and D’ (4.5, 1.5)

Now plot these points in a graph and join all the vertices A’B’C’D’.

Dilatation 3

Square A’B’C’D’ is the dilatation of square ABCD with the scale factor 2.

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These are the examples of Preparation for Dilatation.

Dilatation is same as the dilation of a figure. Dilatation is the process of transforming the given figure with the corresponding scale factor. If the size of the scale factor is greater than one then the dilatation is the enlarging of a given figure and if the scale factor is less than one then the dilatation is the compression of a given figure. If the scale factor is 0 then the image will display as it is.

Example problem – Solving dilatation:

Example 1 – Solving dilatation:

Find the dilatation for a figure whose vertices are A(2, 3) , B(4, 4) and C(5, 3) with the scale factor 1/ 2 .

Solution:

The vertices of a given figure is A(2, 3) , B(4, 4) and C(5, 3)

The given scale factor is 1/ 2 which is less than 1. So the dilatation is a compression of a given figure.

Now multiply the x and y coordinates of vertices by scale factor 1 / 2 to get the new vertices of a dilatation.

A(2, 3) = A’(2* 1/ 2 , 3* 1/ 2 ) = A’(1, 1.5)

B(4, 4) = B’(4* 1/ 2 , 4* 1/ 2 ) = B’(2, 2)

C(5, 3) = C’(5* 1/ 2 , 3* 1/ 2 ) = C’(2.5, 1.5)

Plot all the vertices on a graph.

Now join the corresponding vertices.

Dilatation of a triangle

One more example problem – Solving dilatation:

Example 2 – Solving dilatation:

Find the dilatation for a figure whose vertices are A(2, 3) , B(4, 2) ,C(3, 1) and D(4, 4) with the scale factor 2.

Solution:

The vertices of a given figure is A(2, 3) , B(4, 2) ,C(3, 1) and D(4, 4)

The given scale factor is 2 which is greater than 1. So the dilatation is a enlargement of a given figure.

Now multiply the x and y coordinates of vertices by scale factor 2 to get the new vertices of dilatation.

A(2, 3) = A’(2* 2, 3* 2)= A’(4, 6)

B(4, 2) = B’(4* 2, 2* 2)= B’(8, 4)

C(3, 1) = C’(3* 2, 1* 2)= C’(6, 2)

D(4, 4)= D’(4* 2, 4* 2)= D’(8, 8)

Plot all the vertices on a graph.

Now join the corresponding vertices.

Dilatation of a quadrilateral

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