Question

find the image of (-1, 3) obtained by translating 2 units down, followed by a rotation of 270° counterclockwise about the origin.
enter the number that belongs in the green box.

Explanation:

Translate the point down

Translate \( (-1, 3) \) down by 2 units.

$$ (x, y) \to (x, y - 2) $$

$$ (-1, 3) \to (-1, 3 - 2) = (-1, 1) $$

Rotate the point counterclockwise

Using the Coordinate Rotation and Rotation Rules knowledge points

$$ (x', y') \to (y', -x') $$

$$ (-1, 1) \to (1, -(-1)) = (1, 1) $$

Identify the green box value

The final coordinates are \( (1, 1) \).
The green box corresponds to the \(x\)-coordinate.

$$ x = 1 $$

Answer:

Enter the number that belongs in the green box: <blank>1</blank>