Math Problem Statement

what is the answer

What is the total number of lines that are perpendicular to line w?

Solution

To determine the number of lines that are perpendicular to line ww, we need to observe the relationship between line ww and the other lines xx, yy, and zz.

  • Two lines are perpendicular if they intersect at a right angle (90 degrees).
  • Looking at the diagram:
    • Line ww is vertical.
    • Line yy is horizontal, meaning it is perpendicular to ww because vertical and horizontal lines form 90-degree angles.
    • Lines xx and zz are diagonal and do not appear to form right angles with line ww.

Therefore, the only line that is perpendicular to line ww is line yy.

Answer: B. 1

Do you want more details or have any questions?

Here are five related questions to expand on this:

  1. What conditions must two lines satisfy to be perpendicular?
  2. How can we determine if diagonal lines are perpendicular to a vertical line?
  3. How would the answer change if line zz were vertical?
  4. Can two non-parallel diagonal lines be perpendicular to each other?
  5. How do we find the angle between two intersecting diagonal lines?

Tip: Always remember that vertical and horizontal lines are perpendicular to each other by definition.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perpendicular Lines

Formulas

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Theorems

Lines are perpendicular if they intersect at a 90-degree angle.

Suitable Grade Level

Grades 6-8