Reflection of Triangle ABC

Oct 13, 2025 by windailys.com 93 views

Introduction

In geometry, reflection is a fundamental concept that involves flipping a shape or object across a line or axis. When a shape is reflected across the y-axis, its x-coordinates change sign, while the y-coordinates remain the same. In this article, we will explore the reflection of triangle ABC across the y-axis and determine the new coordinates for triangle A'B'C'.

Understanding Reflection Across the Y-Axis

To reflect a point across the y-axis, we need to change the sign of its x-coordinate while keeping the y-coordinate the same. This is because the y-axis is a vertical line that divides the coordinate plane into two parts: the left and right sides. When a point is reflected across the y-axis, it moves from one side of the axis to the other.

Reflection of Triangle ABC

Triangle ABC has vertices A(-3, -1), B(-1, -2), and C(-2, -3). To reflect this triangle across the y-axis, we need to change the sign of the x-coordinates of each vertex while keeping the y-coordinates the same.

Reflection of Vertex A

The x-coordinate of vertex A is -3. To reflect this point across the y-axis, we change the sign of the x-coordinate to 3. The y-coordinate remains the same, which is -1. Therefore, the new coordinates of vertex A' are (3, -1).

Reflection of Vertex B

The x-coordinate of vertex B is -1. To reflect this point across the y-axis, we change the sign of the x-coordinate to 1. The y-coordinate remains the same, which is -2. Therefore, the new coordinates of vertex B' are (1, -2).

Reflection of Vertex C

The x-coordinate of vertex C is -2. To reflect this point across the y-axis, we change the sign of the x-coordinate to 2. The y-coordinate remains the same, which is -3. Therefore, the new coordinates of vertex C' are (2, -3).

Conclusion

In conclusion, the new coordinates for triangle A'B'C' after the reflection across the y-axis are A'(3, -1), B'(1, -2), and C'(2, -3). This transformation involves changing the sign of the x-coordinates of each vertex while keeping the y-coordinates the same.

Answer Options

Based on the reflection of triangle ABC across the y-axis, the correct answer options are:

A. A(-3, 1), B(-1, 2), C(-2, 3) - Incorrect
B. A(-3, 1), B(-1, 0), C(-2, 1) - Incorrect
C. A(3, -1), B(1, -2), C(2, -3) - Correct

Q1: What is reflection across the y-axis?

A1: Reflection across the y-axis is a transformation that involves flipping a shape or object across a vertical line, which is the y-axis. This transformation changes the sign of the x-coordinates of each point while keeping the y-coordinates the same.

Q2: How do I reflect a point across the y-axis?

A2: To reflect a point across the y-axis, you need to change the sign of its x-coordinate while keeping the y-coordinate the same. For example, if a point has coordinates (x, y), its reflection across the y-axis will have coordinates (-x, y).

Q3: What happens to the y-coordinates of a shape when it is reflected across the y-axis?

A3: The y-coordinates of a shape remain the same when it is reflected across the y-axis. Only the x-coordinates change sign.

Q4: Can a shape be reflected across the y-axis more than once?

A4: Yes, a shape can be reflected across the y-axis more than once. Each reflection will change the sign of the x-coordinates of each point, resulting in a new shape.

Q5: How do I determine the new coordinates of a shape after it is reflected across the y-axis?

A5: To determine the new coordinates of a shape after it is reflected across the y-axis, you need to change the sign of the x-coordinates of each point while keeping the y-coordinates the same.

Q6: What is the effect of reflecting a shape across the y-axis on its x-intercepts?

A6: Reflecting a shape across the y-axis will change the sign of the x-intercepts of the shape. If a shape has x-intercepts at (x1, 0) and (x2, 0), its reflection across the y-axis will have x-intercepts at (-x1, 0) and (-x2, 0).

Q7: Can a shape be reflected across the y-axis and then translated?

A7: Yes, a shape can be reflected across the y-axis and then translated. The reflection will change the sign of the x-coordinates of each point, and the translation will move the shape horizontally.

Q8: How do I graph a shape that has been reflected across the y-axis?

A8: To graph a shape that has been reflected across the y-axis, you need to change the sign of the x-coordinates of each point while keeping the y-coordinates the same. Then, plot the new points on the coordinate plane.

Q9: What is the difference between reflecting a shape across the y-axis and reflecting it across the x-axis?

A9: Reflecting a shape across the y-axis changes the sign of the x-coordinates of each point, while reflecting it across the x-axis changes the sign of the y-coordinates of each point.

Q10: Can a shape be reflected across the y-axis and then rotated?

A10: Yes, a shape can be reflected across the y-axis and then rotated. The reflection will change the sign of the x-coordinates of each point, and the rotation will change the orientation of the shape.

Conclusion

In conclusion, reflection across the y-axis is a fundamental concept in geometry that involves flipping a shape or object across a vertical line. By understanding how to reflect a shape across the y-axis, you can solve a variety of problems in mathematics and other fields.