Question:
Triangle ABC, with coordinates A(2, 3), B(3, 5), C(7, 4), is dilated by a scale factor of 2. What are the coordinates of the dilated figure, triangle A′B′C′?
Answer:
![A' =(4,6)](https://tex.z-dn.net/?f=A%27%20%3D%284%2C6%29)
![B' = (6,10)](https://tex.z-dn.net/?f=B%27%20%3D%20%286%2C10%29)
![C' = (14,8)\\](https://tex.z-dn.net/?f=C%27%20%3D%20%2814%2C8%29%5C%5C)
Step-by-step explanation:
Given
![A = (2,3)](https://tex.z-dn.net/?f=A%20%3D%20%282%2C3%29)
![B = (3,5)](https://tex.z-dn.net/?f=B%20%3D%20%283%2C5%29)
![C =(7,4)](https://tex.z-dn.net/?f=C%20%3D%287%2C4%29)
-- Scale factor
Required
Determine the coordinates of A'B'C'
This is calculated by:
![A'B'C' = n * ABC](https://tex.z-dn.net/?f=A%27B%27C%27%20%3D%20n%20%2A%20ABC)
For A':
Substitute values for n and A
![A' =n * A](https://tex.z-dn.net/?f=A%27%20%3Dn%20%2A%20A)
![A' =2 * (2,3)](https://tex.z-dn.net/?f=A%27%20%3D2%20%2A%20%282%2C3%29)
![A' =(4,6)](https://tex.z-dn.net/?f=A%27%20%3D%284%2C6%29)
For B':
Substitute values for n and B
![B' = n * B](https://tex.z-dn.net/?f=B%27%20%3D%20n%20%2A%20B)
![B' = 2 * (3,5)](https://tex.z-dn.net/?f=B%27%20%3D%202%20%2A%20%283%2C5%29)
![B' = (6,10)](https://tex.z-dn.net/?f=B%27%20%3D%20%286%2C10%29)
For C':
Substitute values for n and C
![C' = n * C](https://tex.z-dn.net/?f=C%27%20%3D%20n%20%2A%20C)
![C' = 2 * (7,4)](https://tex.z-dn.net/?f=C%27%20%3D%202%20%2A%20%287%2C4%29)
![C' = (14,8)](https://tex.z-dn.net/?f=C%27%20%3D%20%2814%2C8%29)