On a coordinate plane, a triangle has points A prime (negative 2, 10), B prime (negative 6, 4), and (negative 10, 8).
What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the line y = x?

(10, –2)
(–10, 2)
(–2, –10)
(2, 10)

To determine the pre-image of vertex \(A'\) given that the image was created by a reflection across the line \(y = x\), we need to understand how coordinates transform under this reflection.

When a point \((x, y)\) is reflected across the line \(y = x\), its coordinates are swapped, transforming it to \((y, x)\).

Given:
\(A' = (-2, 10)\)

Let's find its pre-image by swapping the coordinates:
\[
(x, y) \rightarrow (y, x)
\]
So, for \(A'\):
\[
(-2, 10) \rightarrow (10, -2)
\]

Thus, the pre-image of vertex \(A'\) is:
\[
(10, -2)
\]

The correct answer is:
\[
\boxed{(10, -2)}
\]

Do you have any questions or would you like more details on this? Here are some related questions for further practice:

1. What is the pre-image of \(B'\) given \(B' = (-6, 4)\) under the reflection across the line \(y = x\)?
2. How do you determine the pre-image of \((3, 7)\) when reflected across the line \(y = x\)?
3. What is the image of \((5, -9)\) when reflected across the line \(y = x\)?
4. If \(C' = (-10, 8)\), what is the pre-image of \(C'\) under the reflection across the line \(y = x\)?
5. What is the general rule for reflecting a point across the line \(y = x\)?
6. How do you find the coordinates of a point after reflecting it across the line \(y = -x\)?
7. What is the pre-image of the point \((12, -15)\) when reflected over the line \(y = x\)?
8. If a triangle has vertices at \((2, 3)\), \((4, 5)\), and \((6, 7)\), what are the coordinates of the reflected triangle across the line \(y = x\)?

**Tip:** When reflecting a point across the line \(y = x\), simply swap the x and y coordinates to get the new position of the point.

Understand how to find the pre-image of vertex A' after it has been reflected across the line y = x. Learn the step-by-step process with examples and practice problems. Suitable for high school students studying coordinate geometry.

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