Step by step
The question
Question: reflect the point P(3, 2) in the x-axis, then rotate it 180°.
P = (3, 2)
= reflect in the x-axis,
= then rotate 180° about O
1 Draw the shape
Put the point on the grid.
2 First: reflect in the x-axis
Reflection in the x-axis: x stays the same, y changes sign.
The rule is: (x, y) goes to (x, −y).
(x, y) → (x, −y)
P(3, 2) goes to P'(3, −2).
P(3, 2) → P'(3, −2)
3 Then: rotate 180°
Rotation 180°: both numbers stay in their places, and both change sign.
The rule is: (x, y) goes to (−x, −y).
(x, y) → (−x, −y)
P'(3, −2) goes to P''(−3, 2).
P'(3, −2) → P''(−3, 2)
Careful!
The second move starts from the new points.
Not from the first point.
Careful: start from P', not from P
So the final image is P''(−3, 2).
P'' = (−3, 2)
4 Check
Let's check in one go.
Put the first rule's answer (x, −y) into the second rule.
We get (−x, y).
(x, y) → (x, −y) → (−x, y)
P goes straight to (−3, 2).
That is P''.
Right!
P(3, 2) → P''(−3, 2)
Let's look back.
First: draw the shape.
Then: reflect in the x-axis.
Then: rotate 180°.
Last: check.
Answer
P'' = (−3, 2)