Subjects geometry

Transformations 0D0D84

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.