Question

What are the vertices of the pre-images in questions 5&6?

Answer 1

Question 5:

We are asked to draw the image of the triangle after a dilation with a scale factor of 1/4

First of all, note down the vertices of the pre-image.

(-8, 4)

(-8, -4)

(4, -4)

Multiple these vertices with the scale factor (1/4) to get the vertices of the image.

`\begin{gathered} (-8\cdot(1)/(4),4\cdot(1)/(4))=(-2,1) \\ (-8\cdot(1)/(4),-4\cdot(1)/(4))=(-2,-1) \\ (4\cdot(1)/(4),-4\cdot(1)/(4))=(1,-1) \end{gathered}`

Finally, let us draw the image after the dilation.

As you can see, this is clearly a reduction in the size of the triangle.

When the scale factor is less than 1 then the dilation always results in the reduction.

Question 6:

We are asked to draw the image of the rectangle after a dilation with a scale factor of 1.5

First of all, note down the vertices of the pre-image.

(-4, 6)

(-4, 1)

(2, 6)

(2, 1)

Multiple these vertices with the scale factor (1.5) to get the vertices of the image.

`\begin{gathered} \mleft(-4\cdot1.5,6\cdot1.5\mright)=(-6,9) \\ (-4\cdot1.5,1\cdot1.5)=(-6,1.5) \\ (2\cdot1.5,6\cdot1.5)=(3,9) \\ (2\cdot1.5,1\cdot1.5)=(3,1.5) \end{gathered}`

Finally, let us draw the image after the dilation

As you can see, this is clearly an enlargement in the size of the rectangle.

When the scale factor is greater than 1 then the dilation always results in the enlargement.