if t(10,-6) is reflected in the line x = 7

When reflecting a point \( T(x, y) \) across a vertical line, such as \( x = 7 \), the \( x \)-coordinate will change, while the \( y \)-coordinate remains the same.

For the point \( T(10, -6) \) reflected over the line \( x = 7 \):

1. The distance from \( x = 10 \) to the line \( x = 7 \) is \( 10 - 7 = 3 \).
2. The reflected point will be 3 units on the other side of \( x = 7 \), so the new \( x \)-coordinate will be \( 7 - 3 = 4 \).
3. The \( y \)-coordinate remains the same at \( -6 \).

Thus, the reflection of the point \( T(10, -6) \) over the line \( x = 7 \) is the point \( T'(4, -6) \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What is the formula to reflect a point over a line like \( y = c \) instead of \( x = c \)?
2. How do you reflect a point over the origin or another arbitrary point?
3. What is the reflection of a point over a slanted line like \( y = x \)?
4. How do reflections in geometry relate to transformations such as rotations or translations?
5. Can you explain how reflections impact shapes like triangles or rectangles?

**Tip:** When reflecting points, always consider the line of reflection and determine how far each coordinate is from the line.

Discover how to reflect the point T(10, -6) across the vertical line x = 7 using the reflection formula. This solution provides a step-by-step explanation suitable for students in Grades 6-8, covering key concepts in geometry and the reflection theorem.

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