A point is translated on the coordinate plane from (4,-8) to (4,-6). Create a function to show this translation. Which function shows the appropriate translation?

Answer 1

To describe the translation from the point \((4, -8)\) to the point \((4, -6)\), we can observe that the x-coordinate remains unchanged (it stays at 4), while the y-coordinate increases from -8 to -6. This indicates a vertical translation upward.

We can define a function that takes a point \((x, y)\) as input and translates it according to the observed changes:

The translation can be represented as:

• The x-coordinate remains the same: \(x' = x\)
• The y-coordinate increases by 2: \(y' = y + 2\)

Thus, the function \(T(x, y)\) which represents this translation can be defined as:

\[ T(x, y) = (x, y + 2) \]

In this case, if we apply the function to the original point (4, -8):

\[ T(4, -8) = (4, -8 + 2) = (4, -6) \]

This confirms that the function \(T(x, y) = (x, y + 2)\) correctly translates the point \((4, -8)\) to \((4, -6)\).