Dianne drew a triangle with coordinates (1, 3), (3, 2), and (4, 2). She drew an image of the triangle with coordinates (−1, 3), (−3, 2), and (−4, 2). Which rule describes the transformation

The original triangle has the coordinates \((1, 3)\), \((3, 2)\), and \((4, 2)\), and the transformed triangle has the coordinates \((-1, 3)\), \((-3, 2)\), and \((-4, 2)\).

To find the rule that describes the transformation, we can observe the change in the coordinates:

- The \(x\)-coordinates of the points have been negated, while the \(y\)-coordinates remain unchanged.

This type of transformation corresponds to a **reflection over the \(y\)-axis**, where every point \((x, y)\) is transformed to \((-x, y)\).

### Therefore, the rule that describes this transformation is:
**Reflection over the \(y\)-axis**.

Would you like more details or further clarification?

---

Here are some related questions to expand your understanding:
1. How would the transformation change if the triangle were reflected over the \(x\)-axis instead?
2. What would happen to the coordinates if the triangle were translated 3 units downwards?
3. How do you determine the rule of transformation for a rotation of 90 degrees around the origin?
4. If the triangle was dilated by a scale factor of 2, what would the new coordinates be?
5. How do you represent transformations using matrix multiplication?

**Tip:** In reflections, the axis over which the reflection occurs determines whether the \(x\)- or \(y\)-coordinates change signs.

Dianne drew a triangle with coordinates (1, 3), (3, 2), and (4, 2). She drew an image of the triangle with coordinates (−1, 3), (−3, 2), and (−4, 2). Which rule describes the transformation?

Discover how to determine the rule of transformation for a triangle with coordinates (1, 3), (3, 2), and (4, 2) reflected over the y-axis. This problem covers key geometric concepts such as reflections and coordinate transformations, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation