Dilation in Math

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Introduction of dilation in math

The center in connection to the dilation can be said to be a fixed point in the given plane. On the basis of the scale factor as well as the center in connection to the dilation, the dilation transformation can be said to be defined. If the specific scale factor is actually more than one, then the particular image stretches. If the specific scale factor can be said to be amidst 0 and 1, then the particular image shrinks.

Properties of Dilation

Certain specific features of the shapes that actually remain unchanged in the course of the dilation transformations can be said to be the following: -

Each angle in relation to the figure can be said to be the same
Midpoints in relation to the sides of the said figure remain the same in the form of the midpoint of the specific dilated shape
Parallel as well as perpendicular lines in the figure continue to be the same as the parallel as well as perpendicular lines of the specific dilated figure
The images continue to be the same

The only specific change in connection to the dilation process is that the particular distance amidst the given points changes. It actually means that the length of the specific sides of the original or initial image as well as the dilated image may vary. There are 2 kinds of dilation processes. They can be said to be the following: -

Horizontal Dilation

The dilation transformation of any function y=f(x) can be said to be dilated horizontally by any scale factor C can be said to be

Y = f(Cx)

This kind of the transformation is known to be a horizontal dilation.

Vertical Dilation

The dilation transformation of any function y=f(x) can be said to be dilated vertically by a scale factor C, which is

Y = C * f(x)

This kind of the transformation can be said to be known as a Vertical dilation.

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Scale Factor Formula

The basic formula, which is actually utilized for the purposes of the calculation of the scale factor can be said to be, Scale factor = Dimension of the new shape ÷ Dimension of the original shape. In the given case, if the original or initial figure is actually scaled up, then, in such instance, the formula is written or inscribed as, Scale factor = Larger figure dimensions ÷ Smaller figure dimensions.

Formula for Dilations

Example of dilation

Example 1: -

Dilation Scale Factor 2:

Let the source or origin (0, 0) be the centre of the dilation in the specific coordinate plane.

Let the ABC be a specific triangle in the given coordinate plane. The points in the coordinate planes can be said to be A(0, 2), B(2, 1), C(-2, -2).

If the specific scale factor is 2, then all the coordinate points of the given original triangle can be said to have been multiplied by the scale factor 2.

Hence, the dilated triangle shall be A’B’C’ as well as the coordinate points that are obtained are actually A’(0, 4), B’(4, 2), C’(-4, -4).

Dilation with the scale factor 2, and then multiply by 2.

(x, y) → (2x, 2y)

Example 2: -

Dilation Scale Factor ½:

One should presume that, the origin (0, 0) be the centre of the dilation in the given coordinate plane.

Let the ABCD be a quadrilateral in the given coordinate plane. The points in the given coordinate planes can be said to be A(-2, 4), B(4, 4), C(2, -2), D(-4, -2)

If the specific scale factor is 1/2, then all the coordinate points of the original triangle can be said to be multiplied by the scale factor 1/2.

Hence, the dilated triangle shall be A’B’C’D’ and the specific coordinate points that are obtained can be said to be A’(-1, 2), B’(2, 2), C’(1, -1), D’(-2, -1)

Example 3: -

Dilation with scale factor 1/2, then multiply by ½:

(x, y) → (1/2x, 1/2y)

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How to Calculate the Scale Factor in Dilation?

The basic formula in relation to the finding of the scale factor in connection to a dilated figure can be said to be: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

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Most Popular FAQs Searched By Students:

Q.1. What is a Scale Factor?

A scale factor is generally a decimal which multiplies or scales some quantity. In the specific equation y = Cx, C can be said to be the scale factor for the x. C can also said to be the coefficient of the x, and might be known as the constant of the proportionality of the y to the x. For instance, doubling the distances corresponds to any scale factor of 2 for distance, while the cutting of any cake in half actually results in the pieces with any scale factor for the volume of 1 half. The basic equation for it can be said to be the image over the preimage.

Q.2. What is Dilation Transformation?

This transformation gives effect to an image that would be the same as the original or initial shape. Although, there would be a difference in the size of the given shape.