A king is at +12 cm from the lower-left corner of a chessboard, and a knight is at +5.0 cm from the same corner along the same straight line. What is the displacement from the king to the knight?
The displacement from the king to the knight is $\Delta x = x_{\text{knight}} - x_{\text{king}} = 5.0\,\text{cm} - 12\,\text{cm} = -7.0\,\text{cm}$. The negative sign means the knight is 7.0 cm in the negative direction (back toward the lower-left corner) from the king.
What the problem is asking
You are given two positions on the same straight line, measured from the same origin (the lower-left corner). Displacement from one piece to the other is found by subtracting their coordinates in the correct order.
Assign positions with a sign convention
Let the lower-left corner be the origin, and take positions measured away from the corner as positive:
- King: $x_K = +12\,\text{cm}$
- Knight: $x_N = +5.0\,\text{cm}$
Compute displacement from king to knight
“From the king to the knight” means final minus initial:
$$ \Delta x = x_{\text{final}} - x_{\text{initial}} = x_N - x_K $$
$$ \Delta x = 5.0 - 12 = -7.0\,\text{cm} $$
Interpreting the negative sign
$-7.0\,\text{cm}$ means you must move 7.0 cm in the negative direction to go from the king to the knight, which is toward the lower-left corner (toward smaller position values).
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