Question

What are the coordinates of the image after this translation: (x, y) → (x + 1, y − 4)?

a) D'(-3, -4), X'(-2, -1), Q'(1, -1), L'(-2, -5)
b) D'(-4, -3), X'(-1, -2), Q'(-1, 1), L'(-5, -2)
c) D'(-2, -5), X'(-1, -2), Q'(4, 3), L'(-2, -1)
d) D'(-4, 0), X'(-3, 3), Q'(0, 3), L'(-3, -1)

Answer 1

The coordinates of the image after the translation (x, y) → (x + 1, y - 4) are found by adding 1 to the x-coordinate and subtracting 4 from the y-coordinate. However, the options provided do not match the translated coordinates, suggesting a possible error in the question or the options.

Step-by-step explanation:

The question asks for the coordinates of the image after a translation. In coordinate geometry, a translation is a transformation that shifts every point of a figure or a space by the same distance in a given direction. In this case, we have the translation (x, y) → (x + 1, y − 4).

To find the translated coordinates, we simply add 1 to the x-coordinate and subtract 4 from the y-coordinate of each given point. Applying this to the provided options, we get:

• For D(-4, 0), after translation it becomes D'(-3, -4).
• For X(-3, 3), after translation it becomes X'(-2, -1).
• For Q(0, 3), after translation it becomes Q'(1, -1).
• For L(-3, 1), after translation it becomes L'(-2, -3).

However, none of the options given match these results. Thus, there might be a mistake in the original question or the options provided.