Question

HELPPP WILL GIVE BRAINLIEST!! How do I construct a line segment whose length is equal to the AVERAGE of the length of the 2 given line segments??? I can only use a compass and a straight edge.

Answer 1

Answer:

  Bisect the segment that is the sum of the given segments

Step-by-step explanation:

You want to construct a line segment whose length is the average of two given line segments.

Solution

You know that the average of two lengths is half their sum. To construct a line that is half the sum ...

1. Construct a segment equal to the sum. For example, from point X on a line, mark XY = AB to the left of X, and XZ = CD to the right of X. Segment YZ will be the sum of AB and CD.
2. Bisect it. Draw arcs above and below YZ with the same radius equal to more than half of YZ. The line through the intersection points of each pair of arcs will be the perpendicular bisector of YZ. If it intersects YZ at Q, then YQ = QZ = average of AB and CD.