Answer:
The coordinates of B' and C' are
and
, respectively.
Step-by-step explanation:
From the Linear Algebra, we define the translation of a given point as:
(1)
Where:
- Original point, dimensionless.
- Translation vector, dimensionless.
- Translated point, dimensionless.
If we know that
and
, then the translation vector is:
(2)
![T(x,y) = (1,-5)-(4,-2)](https://tex.z-dn.net/?f=T%28x%2Cy%29%20%3D%20%281%2C-5%29-%284%2C-2%29)
![T(x,y) = (-3,-3)](https://tex.z-dn.net/?f=T%28x%2Cy%29%20%3D%20%28-3%2C-3%29)
If we know that
,
and
, then the translated points are, respectively:
(3)
![B'(x,y) = (7,-4) +(-3,-3)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%287%2C-4%29%20%2B%28-3%2C-3%29)
![B'(x,y) = (4, -7)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%284%2C%20-7%29)
![C'(x,y) = C(x,y) +T(x,y)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20C%28x%2Cy%29%20%2BT%28x%2Cy%29)
![C'(x,y) = (-1, -8)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%28-1%2C%20-8%29)
The coordinates of B' and C' are
and
, respectively.