Translate a Triangle on the Coordinate Plane

🛠️ Related Tools

🔑 Key Concepts

  • A translation slides a figure without turning, flipping, or resizing it.
  • The rule \(+7\) in the \(x\)-direction means add 7 to each \(x\)-coordinate.
  • The rule \(-8\) in the \(y\)-direction means subtract 8 from each \(y\)-coordinate.
  • The preimage and image are congruent because translations are rigid transformations.

💡 Main Idea

To translate a figure on the coordinate plane, apply the same change to every point. For this example, each point moves 7 units right and 8 units down.

✏️ Worked Example

🧠 Math Vocabulary

  • Translation: A transformation that slides a figure from one location to another.
  • Slide: An informal word for a translation.
  • Preimage: The original figure before a transformation.
  • Image: The new figure after a transformation.
  • Rigid Transformation: A transformation that preserves size and shape.
  • Non-Rigid Transformation: A transformation that changes size or shape, such as a dilation with a scale factor not equal to 1.
  • Congruent Figures: Figures with the same size and same shape.

📚 What You Should Already Know

Students should know how to plot ordered pairs, identify the positive and negative directions on the coordinate plane, and add or subtract integers.

🚀 What Comes Next

After translations, students can compare other transformations, including reflections, rotations, dilations, and sequences of transformations.

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