Answer:
The rule of dilation is
.
The vertices of the dilated triangle are
,
and
, respectively.
Step-by-step explanation:
From Linear Algebra, we define the dilation by the following definition:
(1)
Where:
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Original point, dimensionless.
- Dilated point, dimensionless.
If we know that
,
,
,
and
, then dilated points of triangle ABC are, respectively:
(2)
![A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]](https://tex.z-dn.net/?f=A%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%203%5Ccdot%20%5B%28-7%2C-6%29-%280%2C0%29%5D)
![A'(x,y) = (-21, -18)](https://tex.z-dn.net/?f=A%27%28x%2Cy%29%20%3D%20%28-21%2C%20-18%29)
(3)
![B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%203%5Ccdot%20%5B%28-5%2C-2%29-%280%2C0%29%5D)
![B'(x,y) = (-15,-10)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%28-15%2C-10%29)
(4)
![C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B3%5Ccdot%20%5B%28-1%2C-5%29-%280%2C0%29%5D)
![C'(x,y) = (-3,-15)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%28-3%2C-15%29)
The rule of dilation is:
(5)
The vertices of the dilated triangle are
,
and
, respectively.