Parallel straight lines are drawn through the ends of segment AB and its middle M, intersecting a certain plane
| February 19, 2021 | education
Parallel straight lines are drawn through the ends of segment AB and its middle M, intersecting a certain plane at points A1, B1, M1. Find the length of segment MM1 if segment AB does not intersect the plane and if: АА1 = 3.6 dm, BB1 = 4.8 dm …
Consider a quadrilateral АА1В1В: АА1 parallel to BB1, АМ = ВМ (M is the middle of AB) and А1М1 = В1М1 (by the property of parallel lines intersecting the plane). Therefore, the quadrilateral АА1В1В is a trapezoid, and ММ1 is its middle line.
The midline is equal to half the sum of the bases of the trapezoid, therefore:
MM1 = (AA1 + BB1) / 2 = (3.6 + 4.8) / 2 = 8.4: 2 = 4.2 (dm).
Answer: the length of the segment MM1 is 4.2 dm.
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