Please enter the coordinate value of the image and our calculator will know the coordinate value of the final Dilation image, with the help of the following step.
Dilation Calculator – The calculator guide provides a free online tool to calculate the centre point coordinate of any modified image after it gets transformed.
What Is Dilation?
In Geometry mathematics, “A particular transformation in the size of an image without changing the original shape of the image is called dilation. Dilation is transformation; in this transformation, the image either enlarge or reduce with the prospect of a particular point C. C is known as the Centre of dilation and scale factor K, which means the ratio of the side where the image increase or decrease.
Types of Dilation:
Mainly we have Four types of dilations.
Enlargement – When images are larger after dilation is called enlargement dilation.
Reduction – When images are smaller after dilation, called reduction dilation
Horizontal dilation – Horizontal Dilation is for a function Y = f(x), Which dilates the given function by C using the given equation.=f(Cx)
Vertical dilation – In the vertical dilation function, y = f(x) dilates vertically with scale C using the given equation Y=C∗f(x).
How Do You Calculate Dilation?
Coordinates of original tringle before dilation
Coordinates of tringle after dilation with the scale factor of 3
With the help of this, you can draw a new triangle without changing the shape. The same work is done in our dilation calculator.
What Is Scale Factor In Dilation?
Scale factor means the exact ratio of size-modified images compared to the original image. It define the transformation in the size of the image.
It defines the change of size in the image
If SF >1, If images get smaller
If 0 < SF < 1, the New image gets shrinked.
If SF = 1, the modified image remains unchanged in shape and size.If 0 < SF < 1, the New image gets shrinked.
If you want to calculate the scale factor, you can use our free online scale factor calculator.
How to Find the Scale Factor of a Dilation?
For the scale factor, we have to find the center point of dilation & count the distance from the center to the pilgrimage point and the center point to point on the image. The ratio between both is called the scale factor.
Enter the value change in x and change in y of a length along with a shape or image pre and post-scaling to calculate the scale factor dilation.
Scale Factor Dilation Formula
This is the formula used to calculate the scale factor dilation of any image or shape.
Scale factor = measurement of the new shape ÷ measurement of the original shape.
SF = X2/X1 = Y2/Y1
Center of Dilation Calculator
Dilation: A dilation is an extension and a reduction in the size and location of a figure or point.
Scale Factor: The scale factor in a dilation is the quantity by which the figure is extended or reduced.
Centre of Dilation: The centre of dilation is a connection point used to scale a figure’s dilation properly. Given a point on the pre-image, (x1,y1)(x1,y1), and a related point on the dilated image, (x2,y2)(x2,y2), and the scale factor, kk, the area of the center of dilation, (xo, yo)(xo, yo) is
(xo=kx1−x2/k−1, yo=ky1−y2/k−1)
How Dilation Calculator Works?
To use the scale factor Dilation calculator, follow these steps.
- Select the number of inputs means the point
- Enter the X & Y coordinates of all points
- Enter dilation value
- Click on calculate button
- Our calculator shows you the final results.
Triangle Dilation Calculator
In Triangle Dilation Calculator, calculate the vertical & horizontal distance of tringle vertices from the centre of dilation and multiply this distance with the scale factor value to get the dilated tringles values.
Example
Use -3 as a scale factor and dilate the point (-1, -7).
ANS
Use the coordinate rule for dilation with k = -3,
(x,y)→(kx,ky)
P(−1,−7)→P′((−3)×(−1),(−3)×(−7))
P(−1,−7)→P′(3,21)
So, the point P(-1, -7) is dilated to the point P’(3, 21).
FAQ
What is the difference between the scale factor ½ and 6?
If you multiply the scale factor ½ by the coordinates of the point of the actual image, the changed image will shrink for sure. But if you multiply the coordinates of the actual image with the scale factor of 6, the final image gets dilated.
What is the use of dilation in the field of chemistry?
In applications like thermal expansion and contraction, dilation has great significance as it is the change in the actual position.
What is the Dilation of 1.5 About the Origin
you must multiply by 1.5 in this case
Soure –