Point is translated units to the left and units down.
A point (5, −2) is translated 3 units to the left and 4 units down. What are the new coordinates?
Answer: A. (2, −6) — A translation moves every point of a figure by the same fixed distance in a given direction, without any rotation or resizing. On the coordinate plane,…
- A.
(2, −6)
- B.
(8, 2)
- C.
(−2, −6)
- D.
(5, −6)
Show answer & explanation
Correct answer: A
A translation moves every point of a figure by the same fixed distance in a given direction, without any rotation or resizing. On the coordinate plane, translating a point some units left subtracts that many units from its x-coordinate (leftward movement decreases x), and translating a point some units down subtracts that many units from its y-coordinate (downward movement decreases y). In general, translating a point (x, y) by 'a' units left and 'b' units down gives the new point (x − a, y − b).
Start with the point (5, −2).
Apply the leftward translation to the x-coordinate: 5 − 3 = 2.
Apply the downward translation to the y-coordinate: −2 − 4 = −6.
Combine the results to get the new coordinates (2, −6).
Reversing the transformation confirms it: starting from (2, −6) and moving 3 units right (+3 to x) and 4 units up (+4 to y) returns exactly to the original point (5, −2), verifying the translation is correct.