https://file.aiquickdraw.com/mathbot/file/1726173651179ib9hwac6.jpg

To reflect the point \( J(4, 10) \) over the line \( y = -x \), we need to apply a transformation that swaps the coordinates of the point and changes their signs. The general rule for reflecting a point \( (x, y) \) over the line \( y = -x \) is:

\[
(x, y) \rightarrow (-y, -x)
\]

For \( J(4, 10) \), applying the rule gives:

\[
(4, 10) \rightarrow (-10, -4)
\]

So, the image of point \( J(4, 10) \) after the reflection is \( (-10, -4) \).

Now, you can plot the point \( (-10, -4) \) on the graph as the reflected point.

Would you like any further explanation or assistance with this?

---

Here are 5 follow-up questions you might explore:
1. How do you derive the reflection formula for any arbitrary line?
2. What would happen if the reflection line was \( y = x \) instead of \( y = -x \)?
3. How would you reflect a point across the y-axis or x-axis?
4. Can a point ever reflect onto itself when reflected over a line?
5. How do transformations like rotation and reflection differ?

**Tip**: When reflecting across a line, visualize the line as a "mirror" and imagine where the image would be in relation to that mirror.

Graph the image of J(4, 10) after a reflection over the line y = -x.

Learn how to reflect the point J(4, 10) over the line y = -x. This problem involves key geometric concepts and the formula (x, y) → (-y, -x) for reflecting points across the line y = -x. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation