Question: STUDENT TASK: ► Plot KITE with vertices: K $(0,2)$ I $(2,4)$ T $(4,2)$ E $(2,0)$ 1. Reflect the kite across the y-axis. ► • Questions: What are the coordinates of K', I', T', and E? Which points change their sign? What do you notice about the shape after reflection? Graph/shape: A kite centered around the point $(2,2)$ with vertices K$(0,2)$, I$(2,4)$, T$(4,2)$, and E$(2,0)$; after reflection across the y-axis, the image is positioned to the top-left/top-right? position_hint=center 3. Rotate the original kite $90^\circ$ clockwise about the origin. • Questions: What are the coordinates after the rotation of K''', I''', T''', and E'''? Did the kite change shape or size? What point remained the reference for the rotation? graph: kite shape rotated $90^\circ$ clockwise about the origin, position_hint=center 2. Translate the reflected kite: 3 units left and 2 units up Questions: Did the shape change in size or orientation? What transformation rule was applied? What are the coordinates of K'', I'', T'', and E''?

1. **State the problem:** We have a kite with vertices $K(0,2)$, $I(2,4)$, $T(4,2)$, and $E(2,0)$. We will perform three transformations: reflection across the y-axis, rotation $90^\circ$ clockwise about the origin, and translation of the reflected kite. --- 2. **Reflection across the y-axis:** - Formula: Reflecting a point $(x,y)$ across the y-axis gives $(-x,y)$. - Apply to each vertex: - $K(0,2) \to K'(\cancel{0},2) = (0,2)$ - $I(2,4) \to I'(-2,4)$ - $T(4,2) \to T'(-4,2)$ - $E(2,0) \to E'(-2,0)$ 3. **Which points change their sign?** - Points with $x \neq 0$ change sign in the $x$-coordinate: $I, T, E$. - Point $K$ remains the same because $x=0$. 4. **Shape after reflection:** - The kite is mirrored across the y-axis. - The shape and size remain the same, only the position changes. --- 5. **Rotation $90^\circ$ clockwise about the origin:** - Formula: Rotating $(x,y)$ $90^\circ$ clockwise gives $(y,-x)$. - Apply to original vertices: - $K(0,2) \to K'''(2,0)$ - $I(2,4) \to I'''(4,-2)$ - $T(4,2) \to T'''(2,-4)$ - $E(2,0) \to E'''(0,-2)$ 6. **Did the kite change shape or size?** - No, rotation preserves shape and size. 7. **Reference point for rotation:** - The origin $(0,0)$ is the center of rotation. --- 8. **Translation of the reflected kite:** - Translation rule: $(x,y) \to (x-3, y+2)$ (3 units left, 2 units up). - Apply to reflected points: - $K'(0,2) \to K''(0-3, 2+2) = (-3,4)$ - $I'(-2,4) \to I''(-2-3, 4+2) = (-5,6)$ - $T'(-4,2) \to T''(-4-3, 2+2) = (-7,4)$ - $E'(-2,0) \to E''(-2-3, 0+2) = (-5,2)$ 9. **Did the shape change in size or orientation?** - No, translation moves the shape without changing size or orientation. 10. **Transformation rule applied:** - Translation by vector $(-3,2)$. --- **Final answers:** - Reflected coordinates: $K'(0,2)$, $I'(-2,4)$, $T'(-4,2)$, $E'(-2,0)$. - Points changing sign in $x$: $I, T, E$. - After reflection, shape is congruent but mirrored. - Rotated coordinates: $K'''(2,0)$, $I'''(4,-2)$, $T'''(2,-4)$, $E'''(0,-2)$. - Rotation preserves shape and size; origin is center. - Translated reflected kite coordinates: $K''(-3,4)$, $I''(-5,6)$, $T''(-7,4)$, $E''(-5,2)$. - Translation preserves size and orientation.