Answer:
The scale factor of dilation is -3
Step-by-step explanation:
* Lets revise the meaning of 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 stretches or shrinks the original figure by a scale factor and
center of dilation
- If the scale factor between 0 and 1, then the original figure shrinks
- If the scale factor greater than 1, then the original figure stretches
- If the scale factor is negative then the original figure is stretches or
shrinks and rotate 180°
* Lets solve the problem
∵ The vertices of the original triangles are
(-4 , -4) , (-4 , -7) , (-6 , -4)
∵ The vertices of the image triangles are
(-4 , -4) , (-4 , 5) , (2 , -4)
∵ The length of one side of the original triangle is (-7) - (-4) = 3 units
∵ The length of the corresponding side in the image triangle is
(5) - (-4) = 9 units
∵ The image is in the opposite side of the center of dilation
- That means the original triangle rotate 180° around the center
of dilation
∴ The scale factor is negative
∵ The ratio between the corresponding sides are 9/3 = 3
∴ <em>The scale factor of dilation is -3</em>
