Respuesta :
Answer:
28 cm
Step-by-step explanation:
dilation means to increase or decrease the shape so find the amount it was dilated by dividing -12 by -3 or 20/5 u should get 4 then multiply 7 by 4.
Option (D) will be the answer.
Dilation of a point or a figure:
- If a point (x, y) is dilated by a scale factor 'k' about the origin, image of the point will be defined by the rule,
(x, y) → (kx, ky)
- If a figure is dilated by a scale factor 'k', rule for the dilation will be,
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the preimage}}[/tex]
Given in the question,
- ΔABC with AB = 3 cm and BC = 7 cm
- Point A(-3, 5) of ΔABC is dilated by a scale factor 'k' about the origin to form the image triangle A'B'C' with A'(-12, 20)
Use the rule of dilation of a point about the origin,
(x, y) → (kx, ky)
A(-3, 5) → (-12, 20)
→ [4(-3), 4(5)]
Therefore, scale factor 'k' = 4.
If the side BC is dilated to form the image side B'C' by a scale factor 'k',
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the preimage}}[/tex]
4 = [tex]\frac{B'C'}{BC}[/tex]
B'C' = 4(BC)
= 4(7)
= 28 cm
Therefore, Option (D) will be the answer.
Learn more about the transformation here,
https://brainly.com/question/2865768?referrer=searchResults
