On this coordinate plane, point A is translated into point A′. Which functions give the two translations?

Answer 1

To determine the functions that represent the translations of point A to point A′ on a coordinate plane, we need to know the coordinates of both points and the direction and distance of the translation.

Let's denote point A by its coordinates \( A(x_A, y_A) \) and point A′ by its coordinates \( A'(x_{A'}, y_{A'}) \). The translation from point A to point A′ can be mathematically expressed in terms of functions for the x-coordinate and y-coordinate as follows:

1. Translation of the x-coordinate: \[ x_{A'} = x_A + t_x \] where \( t_x \) is the horizontal translation distance (could be positive or negative, depending on the direction).

2. Translation of the y-coordinate: \[ y_{A'} = y_A + t_y \] where \( t_y \) is the vertical translation distance (also could be positive or negative).

Thus, the functions describing the translation can generally be expressed as: \[ f(x) = x + t_x \] \[ g(y) = y + t_y \]

Without the specific coordinates of points A and A′, we can't provide the actual values for \( t_x \) and \( t_y \). However, if you can provide the coordinates of points A and A′, I can help calculate the specific translation values.

Answer 2

A is on the 3,-3 ans a' is on the 3,5

Answer 3

Given the coordinates:

• Point \( A(3, -3) \)
• Point \( A'(3, 5) \)

We can find the translations in the x and y directions.

1. Translation of the x-coordinate:

   • The x-coordinate remains the same.
   • Thus, the translation for the x-coordinate is: \[ x_{A'} = x_A + t_x \implies 3 = 3 + t_x \implies t_x = 0 \]

2. Translation of the y-coordinate:

   • The y-coordinate changes from -3 to 5.
   • Thus, the translation for the y-coordinate is: \[ y_{A'} = y_A + t_y \implies 5 = -3 + t_y \implies t_y = 5 + 3 = 8 \]

Now, we have our translations:

• The function for the x-coordinate is: \[ f(x) = x + 0 = x \]

• The function for the y-coordinate is: \[ g(y) = y + 8 \]

In summary, the translations from point A to point A′ can be represented by the following functions:

• X translation: \( f(x) = x \) (no change)
• Y translation: \( g(y) = y + 8 \) (an upward translation of 8 units)