Finding the Reflection of a Point on the Y-axis

Understanding reflections in geometry is a fundamental concept. When a point is reflected across an axis, its position changes in a predictable way based on that axis.

Rule for Reflection on the Y-axis

The reflection of a point \((x, y)\) on the Y-axis results in a new point with coordinates \((-x, y)\). This means the x-coordinate changes its sign, while the y-coordinate remains unchanged.

Applying the Rule to Point \((-2, -6)\)

We are given the point \((-2, -6)\). To find its reflection on the Y-axis, we apply the rule \((x, y) \to (-x, y)\):

• The original x-coordinate is \(-2\). Changing its sign gives \(-(-2) = 2\).
• The original y-coordinate is \(-6\). This remains the same.

Therefore, the reflection of the point \((-2, -6)\) on the Y-axis is \((2, -6)\).

Comparing with the Options

Let's look at the given options:

• Option 1: \((2, 6)\) - Incorrect, the y-coordinate changed sign.
• Option 2: \((-6, -2)\) - Incorrect, coordinates are swapped and signs are wrong.
• Option 3: \((-2, 6)\) - Incorrect, only the y-coordinate changed sign.
• Option 4: \((2, -6)\) - Correct, the x-coordinate's sign changed, and the y-coordinate remained the same.

The calculated reflection \((2, -6)\) matches Option 4.

Revision Table: Summary of Reflections

Additional Information on Geometric Transformations

Reflection is one type of geometric transformation. Other common transformations include translation (sliding the point without changing orientation), rotation (turning the point around a fixed point), and dilation (resizing the shape). Each transformation follows specific rules for changing the coordinates of a point.

Understanding these rules is crucial for solving problems involving coordinate geometry and transformations.