What is the image point of left parenthesis, minus, 3, comma, minus, 2, right parenthesis(−3,−2) after the transformation r, start subscript, x-axis, end subscript, circle, R, start subscript, 270, degrees, end subscriptr
x-axis
​
∘R
270
∘

To solve the transformation of the point \((-3, -2)\) under the combined transformations of reflection across the \(x\)-axis \((r_{x-axis})\) and a rotation of \(270^\circ\) counterclockwise \((R_{270^\circ})\), we need to break down the process into two steps:

1. **Reflection across the \(x\)-axis**:
   The reflection across the \(x\)-axis transforms a point \((x, y)\) to \((x, -y)\).
   - For the point \((-3, -2)\), after reflecting across the \(x\)-axis:
     \[
     r_{x-axis}(-3, -2) = (-3, 2)
     \]

2. **Rotation by \(270^\circ\) counterclockwise**:
   A \(270^\circ\) counterclockwise rotation transforms a point \((x, y)\) to \((y, -x)\).
   - Applying this rotation to the point \((-3, 2)\) (the result of the reflection):
     \[
     R_{270^\circ}(-3, 2) = (2, 3)
     \]

Thus, the image of the point \((-3, -2)\) after the combined transformation \(r_{x-axis} \circ R_{270^\circ}\) is **(2, 3)**.

Would you like further details on this process? 

Here are 5 related questions to deepen your understanding:
1. How does a rotation of \(90^\circ\) counterclockwise differ from \(270^\circ\)?
2. What is the general formula for reflecting a point across the \(y\)-axis?
3. What happens when a point is rotated \(180^\circ\) counterclockwise?
4. How does the combination of transformations affect the overall result?
5. What would the point be after only applying the reflection without the rotation?

**Tip:** Always apply transformations in the correct order, as reversing them can yield different results.

What is the image point of (-3, -2) after the transformation r_x-axis ∘ R_270°?

Learn how to find the image point of (-3, -2) after a reflection across the x-axis and a 270° counterclockwise rotation. This detailed step-by-step solution covers key geometry concepts and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation