1. **Reflect the pre-image over the x-axis.**
The reflection rule over the x-axis is given by:
$$ (x,y) \to (x,-y) $$
This means the x-coordinate stays the same, and the y-coordinate changes sign.
If the original points are $K(x_1,y_1)$, $L(x_2,y_2)$, and $M(x_3,y_3)$, then their reflections are:
$$ K'(x_1,-y_1), L'(x_2,-y_2), M'(x_3,-y_3) $$
2. **Rotate the figure 90° counter-clockwise about the origin.**
The rotation rule for 90° CCW is:
$$ (x,y) \to (-y,x) $$
Applying this to points $N(x_4,y_4)$ and $O(x_5,y_5)$:
$$ N'(-y_4,x_4), O'(-y_5,x_5) $$
3. **Translate the figure up 4 and to the left 3.**
The translation rule is:
$$ (x,y) \to (x-3,y+4) $$
For points $P(x_6,y_6)$, $Q(x_7,y_7)$, $R(x_8,y_8)$, and $S(x_9,y_9)$:
$$ P'(x_6-3,y_6+4), Q'(x_7-3,y_7+4), R'(x_8-3,y_8+4), S'(x_9-3,y_9+4) $$
**Ordinates on the graph** refer to the y-coordinates of points. After each transformation, the ordinates change as follows:
- Reflection over x-axis: $y$ becomes $-y$
- Rotation 90° CCW: $y$ becomes the new $x$-coordinate, and $x$ becomes the new $y$-coordinate
- Translation up 4: $y$ increases by 4
This completes the transformations with rules, labels, and coordinate changes.
Transformations 0D0D84
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