What is the image point of left parenthesis, 0, comma, 7, right parenthesis(0,7) after the transformation T, start subscript, 3, comma, 0, end subscript, circle, r, start subscript, y, equals, minus, x, end subscriptT 
3,0
​
 ∘r 
y=−x
​
 ?

To find the image point of \((0,7)\) after the transformation \(T_{3,0} \circ r_{y=-x}\), let's break down the process step by step.

### Step 1: Apply the reflection \(r_{y=-x}\)
The transformation \(r_{y=-x}\) reflects a point across the line \(y = -x\). The rule for this reflection is:
\[
(x, y) \rightarrow (-y, -x)
\]
So, applying this reflection to the point \((0, 7)\), we get:
\[
(0, 7) \rightarrow (-7, 0)
\]

### Step 2: Apply the translation \(T_{3,0}\)
The translation \(T_{3,0}\) moves a point 3 units to the right and 0 units up. The rule for this transformation is:
\[
(x, y) \rightarrow (x + 3, y + 0)
\]
So, applying this translation to the point \((-7, 0)\), we get:
\[
(-7, 0) \rightarrow (-7 + 3, 0 + 0) = (-4, 0)
\]

### Final Answer:
The image point of \((0, 7)\) after the transformation \(T_{3,0} \circ r_{y=-x}\) is \((-4, 0)\).

Would you like any more details or clarifications on this?

---

Here are 5 related questions:
1. What is the reflection across the line \(y = x\)?
2. How would the point change if we reflect it across the x-axis?
3. Can a transformation be a combination of reflection and rotation?
4. How would the point \((3,4)\) transform under \(T_{5,2} \circ r_{y=-x}\)?
5. What is the result of translating a point by \((-2, -3)\)?

**Tip:** When working with multiple transformations, apply them in the correct order—this can affect the final result!

What is the image point of (0,7) after the transformation T_{3,0} ∘ r_{y=-x}?

Learn how to find the image point of (0,7) after applying the transformation T_{3,0} followed by the reflection r_{y=-x}. This problem covers transformations in coordinate geometry, including reflections and translations. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation