Triangle $ABC$ is translated to triangle $A'B'C'$. We need to find the coordinates of $B'$ and $C'$.

1. Problem Description

Triangle $ABC$ is translated to triangle $A'B'C'$. We need to find the coordinates of $B'$ and $C'$.

2. Solution Steps

First, we determine the coordinates of points $A$ and $A'$:

$A = (6, 8)$

$A' = (2, 5)$

To find the translation vector, we subtract the coordinates of $A$ from the coordinates of $A'$:

Translation vector $= A' - A = (2, 5) - (6, 8) = (2 - 6, 5 - 8) = (-4, -3)$

This means that the translation is 4 units to the left and 3 units down.

Next, we find the coordinates of points $B$ and $C$:

$B = (8, 8)$

$C = (9, 6)$

Now we apply the translation vector to points $B$ and $C$ to find the coordinates of $B'$ and $C'$.

$B' = B + \text{translation vector} = (8, 8) + (-4, -3) = (8 - 4, 8 - 3) = (4, 5)$

$C' = C + \text{translation vector} = (9, 6) + (-4, -3) = (9 - 4, 6 - 3) = (5, 3)$

3. Final Answer

The coordinates of $B'$ are $(4, 5)$ and the coordinates of $C'$ are $(5, 3)$.