Question

Compare a dilation to the other transformations: translation, reflection, rotation.

Answer 1

Dilation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

• A dilation that creates a larger image is called an enlargement.

• A dilation that creates a smaller image is called a reduction.

• A dilation stretches or shrinks the original figure.

it could also be seen with the help of figure attached to the answer.

Translation:

the translation is the shift of the graph either upward or downward, left or right.

it could also be seen from the figure attached to the answer.

Reflection:

A reflection can be thought of as folding or "flipping" an object over the line of reflection.

• The original object is called the pre-image, and the reflection is called the image.

the figure is attached to the answer.

Rotation:

Rotating shapes means moving them around a fixed point (clockwise or anticlockwise, and by a certain number of degrees). The shape itself stays exactly the same, but its position in the space will change.

Answer 2

We know that there are four types of rigid transformations namely Dilation, Translation, Reflection and Rotation.

Now, Dilation is the transformation that changes the size of the figure by some scale factor i.e. it is the transformation that increases or decreases the size of the given figure.

We can see in the first figure that the triangle ABC is dilated ( increased by some scale factor ) to form A'B'C'.

Further, Translation is the transformation that slides the figure horizontally or vertically to a fixed distance.

The second figure shows the change of position of the solid ABCD to the position of A'B'C'D'.

Now, Reflection is the transformation that flips the image about a straight line.

During reflection, the size of the figure remains same but the it goes to the opposite side of the line.

We can see from the third figure the reflection of ABC about the y-axis to form A'B'C'.

Finally, Rotation is the transformation that turns the image about a fixed point called the center of rotation to a certain degree.

So, in the last figure, we see that the image A is rotated about the center of rotation by 120° to form A'.

Hence, we see that Dilation is different from the other transformations.