Question

1. the coordinate grid shows a pentagon. the pentagon is translated 1 unit to the left and 10 units down to create a new pentagon.

which rule describes this transformation?

• $(x,y) \to (x - 1, y - 10)$
• $(x,y) \to (x + 1, y - 10)$
• $(x,y) \to (x - 1, y + 10)$
• $(x,y) \to (x + 1, y + 10)$

Explanation:

Step1: Recall translation rules

In coordinate geometry, translating a point \((x,y)\) left or right affects the \(x\)-coordinate, and translating up or down affects the \(y\)-coordinate. Moving left by \(a\) units means subtracting \(a\) from the \(x\)-coordinate (\(x - a\)), and moving down by \(b\) units means subtracting \(b\) from the \(y\)-coordinate (\(y - b\)).

Step2: Apply to the problem

The pentagon is translated 1 unit left (so \(x\)-coordinate: \(x - 1\)) and 10 units down (so \(y\)-coordinate: \(y - 10\)). Thus, the transformation rule is \((x,y)\to(x - 1,y - 10)\).

Answer:

\((x,y)\to(x - 1,y - 10)\) (the first option with the filled circle)