If the vector A = (2, 3) is reflected across the line y = x, what is the resulti

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Question: If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?

Options:

Correct Answer: (3, 2)

Solution:

Reflection across y = x gives vector (3, 2).

If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?

If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?

Step 1: Understand what the vector A = (2, 3) means. It has an x-coordinate of 2 and a y-coordinate of 3.
Step 2: Identify the line y = x. This line means that for any point on it, the x-coordinate is equal to the y-coordinate.
Step 3: To reflect a point across the line y = x, you swap the x and y coordinates.
Step 4: Apply the reflection to vector A = (2, 3). Swap the coordinates: the new x-coordinate will be 3 and the new y-coordinate will be 2.
Step 5: Write the resulting vector after reflection. The new vector is (3, 2).

Vector Reflection – Understanding how to reflect a vector across a line, specifically the line y = x, which involves swapping the x and y coordinates.