https://file.aiquickdraw.com/mathbot/file/17302810738829wdqm2or.jpg

ΔABC will be reflected over the y-axis. Then it will be translated according to the rule: T(2, ‒8).
Write the coordinates of ΔA'B'C' and ΔA"B"C".

To solve this, let's go through the steps one by one:

### Step 1: Identify the coordinates of points A, B, and C
From the graph:
- \( A = (1, 5) \)
- \( B = (4, 3) \)
- \( C = (3, 7) \)

### Step 2: Reflect over the y-axis
Reflecting each point over the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same.

- \( A' = (-1, 5) \)
- \( B' = (-4, 3) \)
- \( C' = (-3, 7) \)

Thus, the coordinates of \( \Delta A'B'C' \) after reflection are:
- \( A' = (-1, 5) \)
- \( B' = (-4, 3) \)
- \( C' = (-3, 7) \)

### Step 3: Apply the translation \( T(2, -8) \)
Now we apply the translation \( T(2, -8) \), which means adding 2 to the x-coordinates and subtracting 8 from the y-coordinates of each point.

1. For \( A' = (-1, 5) \):
   - \( A'' = (-1 + 2, 5 - 8) = (1, -3) \)

2. For \( B' = (-4, 3) \):
   - \( B'' = (-4 + 2, 3 - 8) = (-2, -5) \)

3. For \( C' = (-3, 7) \):
   - \( C'' = (-3 + 2, 7 - 8) = (-1, -1) \)

The coordinates of \( \Delta A''B''C'' \) after both transformations are:
- \( A'' = (1, -3) \)
- \( B'' = (-2, -5) \)
- \( C'' = (-1, -1) \)

### Summary:
- **Coordinates of \( \Delta A'B'C' \)** (after reflection):  
  \( A' = (-1, 5) \), \( B' = (-4, 3) \), \( C' = (-3, 7) \)
- **Coordinates of \( \Delta A''B''C'' \)** (after translation):  
  \( A'' = (1, -3) \), \( B'' = (-2, -5) \), \( C'' = (-1, -1) \)

Would you like further explanation on any of these steps?

### Additional Questions to Explore:
1. What is the effect of reflecting a shape over the x-axis instead of the y-axis?
2. How would the coordinates change if the translation rule was \( T(-2, 8) \) instead?
3. How do you find the distance between two points on a coordinate plane?
4. What would happen if we first translated and then reflected the triangle?
5. How can you determine the area of \( \Delta A''B''C'' \)?

### Tip:
When performing transformations, remember to apply each step systematically—starting with reflections or rotations and following up with translations if they are sequential.

ΔABC will be reflected over the y-axis. Then it will be translated according to the rule: T(2, ‒8). Write the coordinates of ΔA'B'C' and ΔA"B"C".

Explore the reflection and translation of triangle ΔABC on the coordinate plane. Learn how to reflect points over the y-axis and apply a translation T(2, -8) to find new coordinates ΔA'B'C' and ΔA"B"C". This problem includes coordinate 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