What transformation results from the equation (x, y) → (x + 5, y - 3)?

What transformation results from the equation (x, y) → (x + 5, y - 3)?

• A. Translation
• B. Reflection
• C. Rotation
• D. Dilation

Answer: (A)

The transformation described by the equation (x, y) → (x + 5, y - 3) represents a translation. In this transformation, each point (x, y) in the plane is moved horizontally and vertically based on the constants added to the x and y coordinates. Specifically, the x-coordinate is increased by 5 units, which means the point shifts to the right, and the y-coordinate is decreased by 3 units, indicating a downward shift. Translations are characterized by moving points without any change in their shape, size, or orientation; they simply shift the entire figure to a new position. This is evident in the equation, as both transformations occur simultaneously, resulting in a new location for each point with no alteration to the figure itself. Other options, such as reflection, rotation, or dilation, involve changing the position through flipping over a line, turning around a point, or resizing respectively, which do not occur in this case. Therefore, the correct characterization of the transformation outlined in the given equation is indeed a translation.

The transformation described by the equation (x, y) → (x + 5, y - 3) represents a translation. In this transformation, each point (x, y) in the plane is moved horizontally and vertically based on the constants added to the x and y coordinates. Specifically, the x-coordinate is increased by 5 units, which means the point shifts to the right, and the y-coordinate is decreased by 3 units, indicating a downward shift.

Translations are characterized by moving points without any change in their shape, size, or orientation; they simply shift the entire figure to a new position. This is evident in the equation, as both transformations occur simultaneously, resulting in a new location for each point with no alteration to the figure itself.

Other options, such as reflection, rotation, or dilation, involve changing the position through flipping over a line, turning around a point, or resizing respectively, which do not occur in this case. Therefore, the correct characterization of the transformation outlined in the given equation is indeed a translation.