Here are the coordinates for the reflected shapes for each problem.
1) Reflection: Across Line $y = -x$
*
Rule: Swap $x$ and $y$, then change both signs $(x, y) \rightarrow (-y, -x)$.
* Original Points: $(-1, -2), (-3, -2), (-3, -4), (-2, -4), (-2, -3), (-1, -3)$
* New Points:
* $(-1, -2) \rightarrow (2, 1)$
* $(-3, -2) \rightarrow (2, 3)$
* $(-3, -4) \rightarrow (4, 3)$
* $(-2, -4) \rightarrow (4, 2)$
* $(-2, -3) \rightarrow (3, 2)$
* $(-1, -3) \rightarrow (3, 1)$
2) Reflection: Across Line $y = x$
*
Rule: Swap $x$ and $y$ $(x, y) \rightarrow (y, x)$.
* Original Points: $(-1, 2), (-3, 3), (-4, 1), (0, 0)$
* New Points:
* $(-1, 2) \rightarrow (2, -1)$
* $(-3, 3) \rightarrow (3, -3)$
* $(-4, 1) \rightarrow (1, -4)$
* $(0, 0) \rightarrow (0, 0)$
3) Reflection: Across the line $x = 1$
*
Rule: The vertical line of reflection is at $x=1$. Find the distance from each point to the line $x=1$ and move that same distance to the other side. Formula: $x' = 2(1) - x = 2 - x$. The $y$ stays the same.
* Original Points: $(1, 4), (4, 4), (4, 2), (2, 2), (2, 3), (1, 3)$
* New Points:
* $(1, 4) \rightarrow (1, 4)$ (On the line)
* $(4, 4) \rightarrow (-2, 4)$ ($4$ is $3$ units right of $1$; go $3$ units left)
* $(4, 2) \rightarrow (-2, 2)$
* $(2, 2) \rightarrow (0, 2)$ ($2$ is $1$ unit right of $1$; go $1$ unit left)
* $(2, 3) \rightarrow (0, 3)$
* $(1, 3) \rightarrow (1, 3)$ (On the line)
4) Reflection: Across the y-axis
*
Rule: Change the sign of the $x$-coordinate $(x, y) \rightarrow (-x, y)$.
* Original Points: $(1, 4), (5, 1), (1, 1)$
* New Points:
* $(1, 4) \rightarrow (-1, 4)$
* $(5, 1) \rightarrow (-5, 1)$
* $(1, 1) \rightarrow (-1, 1)$
5) Reflection: Across the line $y = 2$
*
Rule: The horizontal line of reflection is at $y=2$. Find the distance from each point to the line $y=2$ and move that same distance to the other side. Formula: $y' = 2(2) - y = 4 - y$. The $x$ stays the same.
* Original Points: $(1, 3), (2, 5), (5, 5), (4, 3)$
* New Points:
* $(1, 3) \rightarrow (1, 1)$ ($3$ is $1$ unit above $2$; go $1$ unit down)
* $(2, 5) \rightarrow (2, -1)$ ($5$ is $3$ units above $2$; go $3$ units down)
* $(5, 5) \rightarrow (5, -1)$
* $(4, 3) \rightarrow (4, 1)$
6) Reflection: Across the x-axis
*
Rule: Change the sign of the $y$-coordinate $(x, y) \rightarrow (x, -y)$.
* Original Points: $(2, -3), (2, -5), (4, -5), (4, -4), (5, -4), (5, -2), (3, -2), (3, -3)$
* New Points:
* $(2, -3) \rightarrow (2, 3)$
* $(2, -5) \rightarrow (2, 5)$
* $(4, -5) \rightarrow (4, 5)$
* $(4, -4) \rightarrow (4, 4)$
* $(5, -4) \rightarrow (5, 4)$
* $(5, -2) \rightarrow (5, 2)$
* $(3, -2) \rightarrow (3, 2)$
* $(3, -3) \rightarrow (3, 3)$
Final Answer:
1) Vertices: $(2, 1), (2, 3), (4, 3), (4, 2), (3, 2), (3, 1)$
2) Vertices: $(2, -1), (3, -3), (1, -4), (0, 0)$
3) Vertices: $(1, 4), (-2, 4), (-2, 2), (0, 2), (0, 3), (1, 3)$
4) Vertices: $(-1, 4), (-5, 1), (-1, 1)$
5) Vertices: $(1, 1), (2, -1), (5, -1), (4, 1)$
6) Vertices: $(2, 3), (2, 5), (4, 5), (4, 4), (5, 4), (5, 2), (3, 2), (3, 3)$
Parent Tip: Review the logic above to help your child master the concept of translation dilation rotation and reflection worksheet.
