How to see it
Coordinates tell you where a point is. Always along first, then up. Along the corridor, then up the stairs. The first number is x, the second is y. Four quadrants: negative x is left of the y axis, negative y is below the x axis. Reflection flips a point to the other side of a mirror line. A translation slides it.
A worked example
Reflect (2, 3) in the y axis. The y axis is a vertical mirror. The point is 2 to the right, so its image is 2 to the left: (−2, 3). A translation of 3 right and 2 down takes (1, 4) to (4, 2).
The common mistake: swapping x and y
The trap is swapping the numbers, so (3, 2) becomes the point at 2 along and 3 up. If a problem gives you (−3, 4), the minus is on x, so you go left.
Try one
Reflect (−3, 4) in the x axis.
- A(3, 4)
- B(4, −3)
- C(−3, −4)
- D(3, −4)
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Right: C, (−3, −4)
The x axis is a horizontal mirror, so y flips sign.