Translation of 3 Vertices up to 3 Units (A) - Free Printable
Educational worksheet: Translation of 3 Vertices up to 3 Units (A). Download and print for classroom or home learning activities.
JPG
500×647
28.4 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1093990
⭐
Show Answer Key & Explanations
Step-by-step solution for: Translation of 3 Vertices up to 3 Units (A)
▼
Show Answer Key & Explanations
Step-by-step solution for: Translation of 3 Vertices up to 3 Units (A)
To solve these translation problems, we need to move each vertex (corner) of the shape according to the instructions. A translation vector like $(x, y)$ tells us how many units to move horizontally ($x$) and vertically ($y$).
* Positive $x$: Move Right
* Negative $x$: Move Left
* Positive $y$: Move Up
* Negative $y$: Move Down
Here is the step-by-step solution for each graph:
Rule: Move every point Left 2 and Down 3.
Let's identify the coordinates of the original triangle's vertices and apply the rule:
* Vertex A (top-left): Original $(-2, 2)$.
* New $x$: $-2 - 2 = -4$
* New $y$: $2 - 3 = -1$
* New Point: $(-4, -1)$
* Vertex B (bottom-left): Original $(-3, -2)$.
* New $x$: $-3 - 2 = -5$
* New $y$: $-2 - 3 = -5$
* New Point: $(-5, -5)$
* Vertex C (right): Original $(2, 2)$.
* New $x$: $2 - 2 = 0$
* New $y$: $2 - 3 = -1$
* New Point: $(0, -1)$
Action: Draw a triangle connecting $(-4, -1)$, $(-5, -5)$, and $(0, -1)$.
---
Rule: Move every point Left 1 and Up 3.
Original Vertices:
* Vertex A (left): $(-2, 2)$
* New $x$: $-2 - 1 = -3$
* New $y$: $2 + 3 = 5$
* New Point: $(-3, 5)$
* Vertex B (bottom): $(1, -4)$
* New $x$: $1 - 1 = 0$
* New $y$: $-4 + 3 = -1$
* New Point: $(0, -1)$
* Vertex C (right): $(1, 1)$
* New $x$: $1 - 1 = 0$
* New $y$: $1 + 3 = 4$
* New Point: $(0, 4)$
Action: Draw a triangle connecting $(-3, 5)$, $(0, -1)$, and $(0, 4)$.
---
Rule: Move every point Right 2 and Up 2.
Original Vertices:
* Vertex A (top): $(-4, 1)$
* New $x$: $-4 + 2 = -2$
* New $y$: $1 + 2 = 3$
* New Point: $(-2, 3)$
* Vertex B (bottom-left): $(-3, -2)$
* New $x$: $-3 + 2 = -1$
* New $y$: $-2 + 2 = 0$
* New Point: $(-1, 0)$
* Vertex C (bottom-right): $(-1, -2)$
* New $x$: $-1 + 2 = 1$
* New $y$: $-2 + 2 = 0$
* New Point: $(1, 0)$
Action: Draw a triangle connecting $(-2, 3)$, $(-1, 0)$, and $(1, 0)$.
---
Rule: Move every point Left 3 and Up 2.
Original Vertices:
* Vertex A (top): $(-1, 4)$
* New $x$: $-1 - 3 = -4$
* New $y$: $4 + 2 = 6$
* New Point: $(-4, 6)$
* Vertex B (left): $(-3, -1)$
* New $x$: $-3 - 3 = -6$
* New $y$: $-1 + 2 = 1$
* New Point: $(-6, 1)$
* Vertex C (right): $(3, -2)$
* New $x$: $3 - 3 = 0$
* New $y$: $-2 + 2 = 0$
* New Point: $(0, 0)$
Action: Draw a triangle connecting $(-4, 6)$, $(-6, 1)$, and $(0, 0)$.
Final Answer:
1. Top-Left Image: Plot points at $(-4, -1)$, $(-5, -5)$, and $(0, -1)$ and connect them to form the new triangle.
2. Top-Right Image: Plot points at $(-3, 5)$, $(0, -1)$, and $(0, 4)$ and connect them to form the new triangle.
3. Bottom-Left Image: Plot points at $(-2, 3)$, $(-1, 0)$, and $(1, 0)$ and connect them to form the new triangle.
4. Bottom-Right Image: Plot points at $(-4, 6)$, $(-6, 1)$, and $(0, 0)$ and connect them to form the new triangle.
* Positive $x$: Move Right
* Negative $x$: Move Left
* Positive $y$: Move Up
* Negative $y$: Move Down
Here is the step-by-step solution for each graph:
1. Top-Left Graph: Translate by $(-2, -3)$
Rule: Move every point Left 2 and Down 3.
Let's identify the coordinates of the original triangle's vertices and apply the rule:
* Vertex A (top-left): Original $(-2, 2)$.
* New $x$: $-2 - 2 = -4$
* New $y$: $2 - 3 = -1$
* New Point: $(-4, -1)$
* Vertex B (bottom-left): Original $(-3, -2)$.
* New $x$: $-3 - 2 = -5$
* New $y$: $-2 - 3 = -5$
* New Point: $(-5, -5)$
* Vertex C (right): Original $(2, 2)$.
* New $x$: $2 - 2 = 0$
* New $y$: $2 - 3 = -1$
* New Point: $(0, -1)$
Action: Draw a triangle connecting $(-4, -1)$, $(-5, -5)$, and $(0, -1)$.
---
2. Top-Right Graph: Translate by $(-1, 3)$
Rule: Move every point Left 1 and Up 3.
Original Vertices:
* Vertex A (left): $(-2, 2)$
* New $x$: $-2 - 1 = -3$
* New $y$: $2 + 3 = 5$
* New Point: $(-3, 5)$
* Vertex B (bottom): $(1, -4)$
* New $x$: $1 - 1 = 0$
* New $y$: $-4 + 3 = -1$
* New Point: $(0, -1)$
* Vertex C (right): $(1, 1)$
* New $x$: $1 - 1 = 0$
* New $y$: $1 + 3 = 4$
* New Point: $(0, 4)$
Action: Draw a triangle connecting $(-3, 5)$, $(0, -1)$, and $(0, 4)$.
---
3. Bottom-Left Graph: Translate by $(2, 2)$
Rule: Move every point Right 2 and Up 2.
Original Vertices:
* Vertex A (top): $(-4, 1)$
* New $x$: $-4 + 2 = -2$
* New $y$: $1 + 2 = 3$
* New Point: $(-2, 3)$
* Vertex B (bottom-left): $(-3, -2)$
* New $x$: $-3 + 2 = -1$
* New $y$: $-2 + 2 = 0$
* New Point: $(-1, 0)$
* Vertex C (bottom-right): $(-1, -2)$
* New $x$: $-1 + 2 = 1$
* New $y$: $-2 + 2 = 0$
* New Point: $(1, 0)$
Action: Draw a triangle connecting $(-2, 3)$, $(-1, 0)$, and $(1, 0)$.
---
4. Bottom-Right Graph: Translate by $(-3, 2)$
Rule: Move every point Left 3 and Up 2.
Original Vertices:
* Vertex A (top): $(-1, 4)$
* New $x$: $-1 - 3 = -4$
* New $y$: $4 + 2 = 6$
* New Point: $(-4, 6)$
* Vertex B (left): $(-3, -1)$
* New $x$: $-3 - 3 = -6$
* New $y$: $-1 + 2 = 1$
* New Point: $(-6, 1)$
* Vertex C (right): $(3, -2)$
* New $x$: $3 - 3 = 0$
* New $y$: $-2 + 2 = 0$
* New Point: $(0, 0)$
Action: Draw a triangle connecting $(-4, 6)$, $(-6, 1)$, and $(0, 0)$.
Final Answer:
1. Top-Left Image: Plot points at $(-4, -1)$, $(-5, -5)$, and $(0, -1)$ and connect them to form the new triangle.
2. Top-Right Image: Plot points at $(-3, 5)$, $(0, -1)$, and $(0, 4)$ and connect them to form the new triangle.
3. Bottom-Left Image: Plot points at $(-2, 3)$, $(-1, 0)$, and $(1, 0)$ and connect them to form the new triangle.
4. Bottom-Right Image: Plot points at $(-4, 6)$, $(-6, 1)$, and $(0, 0)$ and connect them to form the new triangle.
Parent Tip: Review the logic above to help your child master the concept of translation graph worksheet.
