Study guides › Level 7 · Geometry

Flips and turns on a grid

Level 7 · Geometry · for questions like “The point (3, 2) is reflected over the x-axis. Where does it land?”

💡 The idea

Move	(x, y) becomes
Flip over the x-axis	(x, −y)
Flip over the y-axis	(−x, y)
Flip over the line y = x	(y, x)
Quarter turn counterclockwise around (0, 0)	(−y, x)
Half turn around (0, 0)	(−x, −y)

1. (3, 2) over the x-axis: (3, −2).

2. (3, 2), a quarter turn counterclockwise: (−2, 3).

3. (−4, 1) over y = x: (1, −4).

Over the x-axis, the y changes. The point flips up or down across the x-axis.
Check a quarter turn with (1, 0): it should land on (0, 1).

Answers: 1) (−5, −2) 2) (−2, −6) 3) (−1, 4)

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