Question

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

Original shape coordinates: D(−4, 0), X(−3, 3), Q(0, 3), L(−3, −1).
a) D(−3, −4), X(−2, −1), Q(1, −1), L(−2, −5)
b) D(−3, −4), X(−2, −1), Q(1, −1), L(−2, −5)
c) D(−4, −4), X(−3, −1), Q(0, −1), L(−3, −5)
d) D(−4, −4), X(−3, −1), Q(0, −1), L(−3, −5)

Answer 1

After applying the translation (x, y) → (x + 1, y - 4) to each of the given coordinates, the new positions of the points are D(-3, -4), X(-2, -1), Q(1, -1), and L(-2, -5), matching options a and b.

Step-by-step explanation:

The student is asking about a translation of the coordinates of a geometric shape in the xy-coordinate system. To find the image coordinates after the translation of (x, y) → (x + 1, y - 4), we add 1 to each x-coordinate and subtract 4 from each y-coordinate of the original shape coordinates.

• For point D(-4, 0), the new coordinates are D(-4 + 1, 0 - 4) which is D(-3, -4).
• For point X(-3, 3), the new coordinates are X(-3 + 1, 3 - 4) which is X(-2, -1).
• For point Q(0, 3), the new coordinates are Q(0 + 1, 3 - 4) which is Q(1, -1).
• For point L(-3, -1), the new coordinates are L(-3 + 1, -1 - 4) which is L(-2, -5).

Therefore, the translated coordinates are D(-3, -4), X(-2, -1), Q(1, -1), L(-2, -5), which corresponds to option a and b in the student's question (which are identical).