Dilation in Geometry: Making Shapes Bigger or Smaller
Dilation is a cool way to change the size of shapes in geometry. It helps us make shapes bigger or smaller while keeping their original look. If you're in Year 7 Mathematics, learning about dilations is important! Let's explore what dilations are, how they work, and check out a few examples.
Dilation is when we change the size of a shape.
It uses two main things:
Center of Dilation: This is the point that the shape will grow from or shrink towards. You could pick a point inside, outside, or even at a corner of the shape.
Scale Factor: This tells us how much we will change the size. If it’s more than 1, the shape gets bigger. If it’s between 0 and 1, the shape gets smaller.
Let’s break it down further:
Center of Dilation: Choose any point as the center where the shape will change size.
Scale Factor: This number tells us how to change the size:
Let’s look at some easy examples to see how dilation works.
Imagine a triangle with points at A(1, 2), B(3, 4), and C(5, 2). We want to make it bigger with a scale factor of 2, using the center at (0, 0).
To find the new points, we multiply each point by the scale factor:
The new points are A'(2, 4), B'(6, 8), and C'(10, 4). Now the triangle is bigger, but it still keeps its shape!
Now, let’s look at a rectangle with corners at D(4, 0), E(4, 2), F(6, 2), and G(6, 0). This time, we want to make it smaller using a scale factor of 1/2, with the center still at (0, 0).
Here’s how it looks:
The new corners are D'(2, 0), E'(2, 1), F'(3, 1), and G'(3, 0). The rectangle is now half the size but is still a rectangle with the same shape!
Using dilations is a great way to change shapes in geometry, making them either larger or smaller. By changing the scale factor and picking a center of dilation, you can create different versions of shapes while keeping their angles and proportions.
Next time you see a shape, think about how you could resize it using dilations! It’s a fun way to understand geometry and adds some creativity to math!
Dilation in Geometry: Making Shapes Bigger or Smaller
Dilation is a cool way to change the size of shapes in geometry. It helps us make shapes bigger or smaller while keeping their original look. If you're in Year 7 Mathematics, learning about dilations is important! Let's explore what dilations are, how they work, and check out a few examples.
Dilation is when we change the size of a shape.
It uses two main things:
Center of Dilation: This is the point that the shape will grow from or shrink towards. You could pick a point inside, outside, or even at a corner of the shape.
Scale Factor: This tells us how much we will change the size. If it’s more than 1, the shape gets bigger. If it’s between 0 and 1, the shape gets smaller.
Let’s break it down further:
Center of Dilation: Choose any point as the center where the shape will change size.
Scale Factor: This number tells us how to change the size:
Let’s look at some easy examples to see how dilation works.
Imagine a triangle with points at A(1, 2), B(3, 4), and C(5, 2). We want to make it bigger with a scale factor of 2, using the center at (0, 0).
To find the new points, we multiply each point by the scale factor:
The new points are A'(2, 4), B'(6, 8), and C'(10, 4). Now the triangle is bigger, but it still keeps its shape!
Now, let’s look at a rectangle with corners at D(4, 0), E(4, 2), F(6, 2), and G(6, 0). This time, we want to make it smaller using a scale factor of 1/2, with the center still at (0, 0).
Here’s how it looks:
The new corners are D'(2, 0), E'(2, 1), F'(3, 1), and G'(3, 0). The rectangle is now half the size but is still a rectangle with the same shape!
Using dilations is a great way to change shapes in geometry, making them either larger or smaller. By changing the scale factor and picking a center of dilation, you can create different versions of shapes while keeping their angles and proportions.
Next time you see a shape, think about how you could resize it using dilations! It’s a fun way to understand geometry and adds some creativity to math!