Which Graph Shows a Dilation

 

In mathematics, dilation is the transformation that changes the size of a shape. It is achieved by multiplying the coordinates of a shape by a scaling factor, which can either be greater than 1 to enlarge the shape or less than 1 to shrink it. Dilation is an essential concept in geometry and is commonly used in various fields, such as engineering, physics, and computer graphics.

 

 

In this article, we will discuss what dilation is, the different types of dilation, and how it can be represented graphically. Specifically, we will focus on the graph that shows a dilation and explain how to create it.

 

 

Dilation is a transformation that changes the size of a shape. It is achieved by multiplying each coordinate of a shape by a scaling factor, which can either be greater than 1 to enlarge the shape or less than 1 to shrink it. The center of dilation is the fixed point about which the shape is enlarged or reduced. When the scaling factor is greater than 1, the shape is enlarged, and when it is less than 1, the shape is reduced.

 

 

The formula for dilation is given by: (x', y') = (kx, ky)

 

 

Where (x, y) are the original coordinates of a point, (x', y') are the new coordinates after dilation, and k is the scaling factor.

 

 

There are two types of dilation: the enlargement and the reduction.

 

 

Enlargement: An enlargement is a dilation that increases the size of a shape. When the scaling factor is greater than 1, the shape is enlarged. The new shape is similar to the original shape, but it is larger. The center of dilation can be inside or outside of the original shape.

 

 

Reduction: A reduction is a dilation that decreases the size of a shape. When the scaling factor is less than 1, the shape is reduced. The new shape is similar to the original shape, but it is smaller. The center of dilation can be inside or outside of the original shape.

 

 

The graph that shows a dilation is a transformation of a shape on a coordinate plane. The original shape is drawn, and then the new shape is drawn after dilation. The center of dilation is marked, and the scaling factor is given. The graph can be used to visualize how dilation changes the size of a shape.

 

 

Step 1: Draw the original shape on a coordinate plane. For example, let us draw a triangle with vertices at (0,0), (2,0), and (0,2).

 

 

Step 2: Mark the center of dilation. The center of dilation can be any point on the coordinate plane. For this example, let us use (0,0) as the center of dilation.

 

 

Step 3: Determine the scaling factor. The scaling factor can be any number greater than 1 for enlargement or less than 1 for reduction. For this example, let us use a scaling factor of 2 for enlargement.

 

 

Step 4: Multiply each coordinate of the original shape by the scaling factor. For the triangle, the new coordinates are:

 

 

(0,0) x 2 = (0,0)

 

 

(2,0) x 2 = (4,0)

 

 

(0,2) x 2 = (0,4)

 

 

Step 5: Draw the new shape on the coordinate plane using the new coordinates. For this example, the new triangle has vertices at (0,0), (4,0), and (0,4).

 

 

Step 6: Connect the vertices of the new shape to create the transformed shape.

 

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