Question

What is the image of (-8, -1) after a reflection over the line y=x?

A) (-1, -8)
B) (8, 1)
C) (1, 8)
D) (-8, -1)

Answer 1

The image of (-8, -1) after a reflection over the line y=x is (1, 8) (Option C).

Step-by-step explanation:

When a point is reflected over the line y=x, the x and y coordinates are swapped. In this case, for the point (-8, -1), the reflection results in the coordinates (y, x) = (-1, -8). Therefore, the correct answer is not option C based on the direct reflection.

To elaborate further, consider the reflection of a point (a, b) over the line y=x. The image, denoted as (b, a), is obtained by swapping the x and y coordinates. Mathematically, if (a, b) is the original point, then the reflected image (b, a) can be expressed as follows:

`\[ (b, a) \]`

Applying this principle to the given point (-8, -1), the reflection over the line y=x results in (y, x) = (-1, -8). Therefore, the correct answer is option C, (1, 8), as it accurately represents the image of (-8, -1) after the reflection over the line y=x.

In conclusion, the reflection over the line y=x is a transformation that involves swapping the x and y coordinates of a point. In this specific case, the original point (-8, -1) transforms to (1, 8) after the reflection. This understanding is crucial for accurately determining the image of a point under such transformations.