To solve these translation problems, we need to find the rule that moves every point of the original shape (pre-image) to its new position (image). A translation rule is written as $(x, y) \rightarrow (x + a, y + b)$, where $a$ is the horizontal change and $b$ is the vertical change.
Here is the step-by-step solution for each problem:
1)
*
Pick a corresponding pair of points: Let's look at the bottom-left corner of the triangle.
* Original Point: $(-3, -2)$
* New Point: $(0, 1)$
*
Calculate the change in x: $0 - (-3) = 3$. So, $x$ increases by 3.
*
Calculate the change in y: $1 - (-2) = 3$. So, $y$ increases by 3.
*
Rule: $(x, y) \rightarrow (x + 3, y + 3)$
2)
*
Pick a corresponding pair of points: Let's look at the top vertex of the triangle.
* Original Point: $(-1, 4)$
* New Point: $(3, 1)$
*
Calculate the change in x: $3 - (-1) = 4$. So, $x$ increases by 4.
*
Calculate the change in y: $1 - 4 = -3$. So, $y$ decreases by 3.
*
Rule: $(x, y) \rightarrow (x + 4, y - 3)$
3)
*
Pick a corresponding pair of points: Let's look at the top-left corner of the rectangle.
* Original Point: $(-4, 2)$
* New Point: $(2, -1)$
*
Calculate the change in x: $2 - (-4) = 6$. So, $x$ increases by 6.
*
Calculate the change in y: $-1 - 2 = -3$. So, $y$ decreases by 3.
*
Rule: $(x, y) \rightarrow (x + 6, y - 3)$
4)
*
Pick a corresponding pair of points: Let's look at the bottom-left corner of the square.
* Original Point: $(-3, -1)$
* New Point: $(1, 3)$
*
Calculate the change in x: $1 - (-3) = 4$. So, $x$ increases by 4.
*
Calculate the change in y: $3 - (-1) = 4$. So, $y$ increases by 4.
*
Rule: $(x, y) \rightarrow (x + 4, y + 4)$
5)
*
Pick a corresponding pair of points: Let's look at the bottom-left corner of the L-shape.
* Original Point: $(-3, -4)$
* New Point: $(2, -1)$
*
Calculate the change in x: $2 - (-3) = 5$. So, $x$ increases by 5.
*
Calculate the change in y: $-1 - (-4) = 3$. So, $y$ increases by 3.
*
Rule: $(x, y) \rightarrow (x + 5, y + 3)$
6)
*
Pick a corresponding pair of points: Let's look at the top vertex of the triangle.
* Original Point: $(1, 3)$
* New Point: $(-2, -2)$
*
Calculate the change in x: $-2 - 1 = -3$. So, $x$ decreases by 3.
*
Calculate the change in y: $-2 - 3 = -5$. So, $y$ decreases by 5.
*
Rule: $(x, y) \rightarrow (x - 3, y - 5)$
Final Answer:
1) $(x, y) \rightarrow (x + 3, y + 3)$
2) $(x, y) \rightarrow (x + 4, y - 3)$
3) $(x, y) \rightarrow (x + 6, y - 3)$
4) $(x, y) \rightarrow (x + 4, y + 4)$
5) $(x, y) \rightarrow (x + 5, y + 3)$
6) $(x, y) \rightarrow (x - 3, y - 5)$
Parent Tip: Review the logic above to help your child master the concept of geometry rotations worksheets.
