Dilation of a Point Calculator
How to use the ‘Dilation of a Point’ Calculator’?
Follow these steps to use the dilation of a point calculator:
Step 1: Enter the coordinates of a point and the scale factor(k) into the respective input boxes.
Step 2: Click on the ‘Solve’ button to obtain the coordinates of the point after dilation.
Step 3: Click on the ‘Show Steps’ button to view the steps of finding the coordinates after dilation and represent the dilation on the coordinate plane.
Step 4: Click on the 
button to enter new inputs and start again.
Step 5: Click on the ‘Example’ button to view the dilation with random input values.
Step 6: Click on the ‘Explore’ button to drag and position the point on the coordinate plane. With the use of sliders, the point can be dilated for various scale factors.
Step 7: When on the ‘Explore’ page, click on the ‘Calculate’ button if you want to go back to the calculator.
What is Dilation?
A dilation is a transformation in which a figure is either enlarged or reduced with respect to a fixed point C, known as the center of dilation, and a scale factor k, which is the ratio of the corresponding sides of the image to the length of its preimage.
What is the Dilation of a Point?
The dilation of a point refers to the relocation of a point on the coordinate plane. This is done by calculating the horizontal and vertical distance from the center of dilation and then multiplying these distances with a scale factor to get the coordinates of the dilated point.
The dilation of points (x, y) with a scale factor k is expressed as: (x, y) \(\rightarrow\) (kx, ky)
The value of k could be an integer, a decimal or a fraction.
Solved Examples
Example 1: Dilate a point A(1, 5) using the scale factor as 4.
Solution:
Use the coordinate rule for dilation with k = 4,
\(\left ( x,y \right )\rightarrow \left ( kx, ky \right )\)
\(P\left ( 1, 5 \right )\rightarrow P’ \left ( 4 \times 1, 4 \times 5 \right )\)
\(P\left ( 1, 5 \right )\rightarrow P'( 4, 20 )\)
So, the point P(1, 5) is dilated to the point P'(4, 20).
Example 2: Dilate the point P(-3, 2) using the scale factor as 3.
Solution:
Use the coordinate rule for dilation with k = 3,
\(\left ( x, y \right )\rightarrow \left ( kx, ky \right )\)
\(P\left ( -3, 2 \right )\rightarrow P’ \left ( 3 \times \left ( -3 \right ), 3 \times 2 \right )\)
\(P\left ( -3, 2 \right )\rightarrow P’ \left ( -9, 6 \right )\)
So, the point P(-3, 2) is dilated to the point P’(-9, 6).
Example 3: Use -2 as a scale factor and dilate the point (2, -5).
Solution:
Use the coordinate rule for dilation with k = -2,
\(\left ( x, y \right )\rightarrow \left ( kx, ky \right )\)
\(P \left ( 2, -5 \right )\rightarrow P’ \left ( \left ( -2 \right )\times2, \left ( -2 \right ) \times \left ( -5 \right )\right )\)
\(P\left ( 2, -5 \right ) \rightarrow P’ \left ( -4, 10 \right )\)
So, the point P(2, -5) is dilated to the point P’(-4, 10).
Example 4: Use -3 as a scale factor and dilate the point (-1, -7).
Solution:
Use the coordinate rule for dilation with k = -3,
\(\left ( x, y \right )\rightarrow \left ( kx, ky \right )\)
\(P\left ( -1, -7 \right ) \rightarrow P’ \left ( \left ( -3 \right ) \times \left ( -1 \right ),\left ( -3 \right ) \times \left ( -7 \right )\right )\)
\(P\left ( -1, -7 \right )\rightarrow P’\left ( 3, 21 \right )\)
So, the point P(-1, -7) is dilated to the point P’(3, 21).
Enlarging or reducing the size of a geometric shape without disturbing its shape is known as dilation. Utilizing the scale factor provided for dilation, aids in changing the size of an object.
A scale factor is a number that defines the transformation of a shape or object. It is the ratio of the measure of dimension of the image to its preimage.
On the basis of the value of scale factor(k), dilation can be related to enlargement or reduction in the size of a shape.
For k > 1, dilation is enlargement in size, and for 0 < k < 1, dilation is reduction in size.
A dilation is a reducing or increasing the size of a shape or object. But translation is the movement of an object or figure along the direction of the x and y axes. In dilation the size of the shape changes, but in translation only the position of a shape changes on the coordinate plane, and not the size.