Final answer:
To determine the length of a line segment on dot paper, count the dots for horizontal or vertical segments, or use the Pythagorean theorem for tilted segments by constructing a right triangle and solving for the hypotenuse.
Step-by-step explanation:
To find the length of a line segment on dot paper, you can employ several different methods depending on the orientation of the segment. For a horizontal or vertical segment, you can simply count the dots along the segment. When the segment is tilted, this approach doesn't work because the dots do not line up along the length of the line. Instead, you need to create a right triangle by drawing two lines that are horizontal and vertical from the end points of the segment to form a right angle. The length of the segment will be the hypotenuse of this triangle. At this point, you will use the Pythagorean theorem, a² + b² = c², to calculate the length of the segment, where 'a' and 'b' are the lengths of the horizontal and vertical legs of the triangle and 'c' is the length of the hypotenuse. You can measure 'a' and 'b' with a ruler if necessary, then solve for 'c' to get the length of the line segment. If the exact lengths are difficult to measure with a ruler, you might approximate using the dots as a reference for each unit of measure.