5. If lines / and m are perpendicular with an intersection of point P, the image a point A, A', both on line / could be either a reflection across line m or a rotation of 180 degrees around point P.
a. True
b. False

The statement is **True**.

Here's why:

- If lines \(\ell\) and \(m\) are perpendicular and intersect at point \(P\), the transformation that takes point \(A\) on line \(\ell\) to point \(A'\) on line \(\ell\) could either be:
  - **A reflection** across line \(m\): This would map \(A\) to a point \(A'\) on the opposite side of \(m\) but still on line \(\ell\), as reflections across perpendicular lines preserve the same distance from the line of reflection.
  - **A 180-degree rotation** around point \(P\): Rotating \(A\) by 180 degrees around point \(P\) would place \(A'\) on line \(\ell\), as a 180-degree rotation around a point on the line preserves the line itself.

Both transformations (reflection across a perpendicular line or rotation by 180 degrees around the intersection point) yield the same result.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the effect of a reflection across a line on the coordinates of a point?
2. How does a 180-degree rotation affect the orientation of geometric shapes?
3. Can perpendicular lines always serve as axes for reflection and rotation symmetries?
4. How can you determine if two lines are perpendicular based on their slopes?
5. What is the general rule for rotating a point around a fixed point?

**Tip**: When reflecting across a line, the distance from the original point to the line is the same as from the reflected point to the line.

If lines ℓ and m are perpendicular with an intersection at point P, the image of point A, A', both on line ℓ could be either a reflection across line m or a rotation of 180 degrees around point P.
 a. True
 b. False

Understand how reflections across perpendicular lines and 180-degree rotations around intersection points work in geometry. This problem highlights key concepts of geometric transformations and their effects on points in space. Suitable for Grades 8-10.

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