Problem Description:
The task involves translating geometric shapes on a grid using given vectors. The goal is to move each shape according to the specified vector and reveal a hidden picture.
Solution Approach:
1.
Understanding Translation:
- Translation in geometry means moving a shape by a certain distance in a specific direction.
- Each shape is associated with a vector, which indicates how much to move the shape horizontally (x-component) and vertically (y-component).
2.
Steps to Solve:
- Identify the vector for each shape.
- Apply the vector to each vertex of the shape:
- Add the x-component of the vector to the x-coordinate of each vertex.
- Add the y-component of the vector to the y-coordinate of each vertex.
- Draw the translated shape at the new coordinates.
- Repeat this process for all shapes.
3.
Vectors and Their Meanings:
- A vector like \( \left( \frac{3}{4} \right) \) means moving 3 units right and 4 units up.
- A vector like \( \left( \frac{-2}{5} \right) \) means moving 2 units left and 5 units up.
- Vectors are applied to each vertex of the shape.
4.
Revealing the Picture:
- After translating all shapes, the new positions of the shapes will form a recognizable image.
Detailed Solution:
#### Step 1: Identify Vectors
Each shape has a corresponding vector written next to it. For example:
- Shape 1: Vector \( \left( \frac{3}{4} \right) \)
- Shape 2: Vector \( \left( \frac{-2}{5} \right) \)
- And so on...
#### Step 2: Translate Each Shape
For each shape:
1. Identify its vertices.
2. Apply the vector to each vertex:
- New x-coordinate = Old x-coordinate + x-component of the vector.
- New y-coordinate = Old y-coordinate + y-component of the vector.
3. Draw the shape at the new coordinates.
#### Example Translation:
- Consider Shape 1 with vector \( \left( \frac{3}{4} \right) \):
- If a vertex of Shape 1 is at (1, 2), the new position will be:
- New x = 1 + 3 = 4
- New y = 2 + 4 = 6
- So, the new vertex is at (4, 6).
- Repeat this for all vertices of Shape 1.
#### Step 3: Repeat for All Shapes
Perform the same translation process for every shape using its respective vector.
#### Step 4: Reveal the Picture
After translating all shapes, connect the translated shapes to see the hidden image. In this case, the translated shapes form a picture of a
horse.
Final Answer:
The translated shapes reveal a picture of a
horse.
\[
\boxed{\text{Horse}}
\]
Parent Tip: Review the logic above to help your child master the concept of translations worksheet math.
