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.
[tex]\begin{gathered} (-8\cdot\frac{1}{4},4\cdot\frac{1}{4})=(-2,1) \\ (-8\cdot\frac{1}{4},-4\cdot\frac{1}{4})=(-2,-1) \\ (4\cdot\frac{1}{4},-4\cdot\frac{1}{4})=(1,-1) \end{gathered}[/tex]
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.
[tex]\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}[/tex]
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.
