Question

John left a scavenger hunt for his friends! He advised his friends to travel 5 blocks west and 3 blocks north. Which translation rule below describes John's instructions?

A. (x, y) → (x + 5, y + 3)
B. (x, y) → (x - 5, y + 3)
C. (x, y) → (x - 5, y - 3)
D. (x, y) → (x + 5, y - 3)

Answer 1

The translation rule corresponding to moving 5 blocks west and 3 blocks north is (x, y) → (x - 5, y + 3), which is option B.

Step-by-step explanation:

The question asks which translation rule represents John's instructions to travel 5 blocks west and 3 blocks north. In the context of a coordinate grid where the positive x-axis represents east and the negative x-axis represents west, moving west is equivalent to decreasing the x-coordinate. Similarly, moving north, which is along the positive y-axis, means increasing the y-coordinate.

Therefore, each westward step decreases the x-coordinate by 1 and each northward step increases the y-coordinate by 1. According to John's instructions to move 5 blocks west and 3 blocks north, the translation rule is:

(x, y) → (x - 5, y + 3)

This matches option B in the question. So, the correct translation of John's instructions is represented by option B.