Given:
The vertices of a triangle are A(-1,-1), B(-1,-5), C(0.5,-5).
The figure is translated 2 units left.
To find:
The vertices and the diagram of the triangle after the given translation.
Solution:
if a figure is translated 2 units left, then
![(x,y)\to (x-2,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28x-2%2Cy%29)
Using the above rule, we get
![A(-1,-1)\to A'(-1-2,-1)](https://tex.z-dn.net/?f=A%28-1%2C-1%29%5Cto%20A%27%28-1-2%2C-1%29)
![A(-1,-1)\to A'(-3,-1)](https://tex.z-dn.net/?f=A%28-1%2C-1%29%5Cto%20A%27%28-3%2C-1%29)
Similarly,
![B(-1,-5)\to B'(-1-2,-5)](https://tex.z-dn.net/?f=B%28-1%2C-5%29%5Cto%20B%27%28-1-2%2C-5%29)
![B(-1,-5)\to B'(-3,-5)](https://tex.z-dn.net/?f=B%28-1%2C-5%29%5Cto%20B%27%28-3%2C-5%29)
And,
![C(0.5, -5)\to C'(0.5-2,-5)](https://tex.z-dn.net/?f=C%280.5%2C%20-5%29%5Cto%20C%27%280.5-2%2C-5%29)
![C(0.5, -5)\to C'(-1.5,-5)](https://tex.z-dn.net/?f=C%280.5%2C%20-5%29%5Cto%20C%27%28-1.5%2C-5%29)
So, the vertices of the triangle after the translation are A'(-3,-1), B'(-3,-5), C'(-1.5,-5).
Therefore, the correct option is B.