The problem involves the translation of a line segment in a Cartesian coordinate system. Here's the breakdown:

We are given:

• The original point $A(-1, 3)$ is translated to $A'(4, -4)$.
• The coordinates of point $B(2, 4)$ need to be translated similarly, and we are asked to find the coordinates of the translated point $B'$.

Step 1: Find the translation vector

The translation from $A$ to $A'$ is: $\text{Translation Vector} = (x' - x, y' - y) = (4 - (-1), -4 - 3) = (5, -7)$

Step 2: Apply the translation to point $B$

Now, apply the same translation vector $(5, -7)$ to point $B(2, 4)$: $B' = (2 + 5, 4 - 7) = (7, -3)$

Answer:

The coordinates of point $B'$ are $(7, -3)$.

Let me know if you'd like further explanation or if you have any questions!

Here are 5 related questions:

1. How do you find the translation vector between two points?
2. What is the effect of applying a translation in the Cartesian coordinate system?
3. Can the translation vector change if the points are located in different quadrants?
4. How do you determine the new coordinates of a point after applying a translation in 3D space?
5. What would happen if we reflected point $A$ instead of translating it?

Tip: Always check that the translation vector is applied to each point correctly—addition for the x-coordinates and y-coordinates.