Translate a polygon with coordinates A(2,5), B(7,10), and C(11,2) by 3 units in the X direction and 4 units in the Y direction.
Understand the Problem
The question is asking to translate a polygon with given coordinates (A, B, C) by specified distances in the x and y directions. The translation involves adding the translation distances to the respective coordinates of each vertex of the polygon.
Answer
The new coordinates will be A'(x₁ + d_x, y₁ + d_y), B'(x₂ + d_x, y₂ + d_y), C'(x₃ + d_x, y₃ + d_y).
Answer for screen readers
The new coordinates after translation will be:
- A' = (x₁ + d_x, y₁ + d_y)
- B' = (x₂ + d_x, y₂ + d_y)
- C' = (x₃ + d_x, y₃ + d_y)
Steps to Solve
- Identify the original coordinates of the polygon Start with the coordinates of the vertices of the polygon. For example, let’s say the coordinates of the vertices are:
- A (x₁, y₁)
- B (x₂, y₂)
- C (x₃, y₃)
- Determine the translation distances Identify the distances to translate the polygon along the x and y directions. Suppose these distances are:
- $d_x$: distance to translate in the x direction
- $d_y$: distance to translate in the y direction
- Apply the translation to each vertex To find the new coordinates for each vertex after translation, you'll add the translation distances to the original coordinates.
The new coordinates will be calculated as follows:
- A' = (x₁ + d_x, y₁ + d_y)
- B' = (x₂ + d_x, y₂ + d_y)
- C' = (x₃ + d_x, y₃ + d_y)
- Write the new coordinates Finally, write down the new coordinates for the vertices A', B', and C': $$ \text{New coordinates: } A'(x₁ + d_x, y₁ + d_y), B'(x₂ + d_x, y₂ + d_y), C'(x₃ + d_x, y₃ + d_y) $$
The new coordinates after translation will be:
- A' = (x₁ + d_x, y₁ + d_y)
- B' = (x₂ + d_x, y₂ + d_y)
- C' = (x₃ + d_x, y₃ + d_y)
More Information
The translation of a polygon simply shifts its position in the coordinate system without changing its shape or size. This is a basic concept in geometry and is useful in computer graphics, animation, and game development.
Tips
- Not applying the translation distances to both x and y coordinates.
- Forgetting to specify or confuse the direction of translation.
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