The scale factor determines how big or small a shape is. What is Dilation Transformation?ĭilations are a kind of transformations in which an object is resized based on a scale factor. The Center of Dilation is a point on a plane from which an object is expanded or contracted. A scale-up factor means the original object's size has increased and a scale-down factor means the object's size has decreased. Scale factor is a number by which the size of any shape or geometrical figure can be changed with respect to its original size. Dilation is possible by using the scale factor which helps in increasing or decreasing the size of the object. Thus, we get the scale factor of 3 from both the coordinates.įAQs on Dilation Geometry What is a Dilation in Geometry?ĭilation is the process of enlarging or reducing the size of a geometrical object without changing its shape.

Now, take the y-coordinate of P' = 9 and the y-coordinate of P = 3.

Substitute the values in the formula: 3 ÷ 1 = 3.

Take the x-coordinate of P' = 3 and the x-coordinate of P = 1.

For example, let us take the dimensions of vertex P (1, 3) and P' (3, 9). In this case, if we divide the coordinates of the new vertices by the coordinates of the original vertices, we can get the scale factor. The scale factor can also be calculated directly by using the formula: Scale factor = Dimension of the new shape ÷ Dimension of the original shape In other words, if the scale factor is k, the coordinates (x,y) are transformed to (kx,ky). Every coordinate of Δ PQRis multiplied by the scale factor of 3 to obtain the enlarged Δ P'Q'R'.

$ratios of similar shapes in geometry$

Therefore, the scale factor in this dilation is 3. As we can see, both the coordinates of R' became thrice the coordinates of R The x-coordinate 1 changed to 3 and the y-coordinate 1 changed to 3. This again shows that both the coordinates of Q' became thrice the coordinates of Q. The x-coordinate 3 changed to 9 and the y-coordinate 1 changed to 3. This shows that both the coordinates of P' became thrice the coordinates of P.

The x-coordinate 1 changed to 3 and the y-coordinate 3 changed to 9. Let us find the scale factor of a triangle with the original dimensions and scaled up dimensions. As seen above, after dilation, the coordinates of ΔPQR changed as follows: The scale factor can be calculated when the original dimension and the changed dimension is given. How to Calculate the Scale Factor in Dilation? In the figure shown below, the triangle is enlarged from the center of dilation which is marked as 'R'. It is the center of dilation from which the objects/figures are expanded or contracted. The resizing happens from a point called the center of dilation. Dilation transforms the size of the figure which may either increase or decrease. In this dilation, the size of the square is increased but the shape remains the same.ĭilation geometry has an important concept referred to as the 'center of dilation'. Observe the following figure which shows the dilation of a square. Contraction - When the size of an object is decreased.Expansion - When the size of an object is increased.The new figure obtained after dilation is called the image and the original image is called the pre-image. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. Dilation is the process of resizing or transforming an object.

Ratios of similar shapes in geometry