Find the distance from the midpoint of segment AB to the plane that does not intersect this segment

Find the distance from the midpoint of segment AB to the plane that does not intersect this segment if the distances from points A and B to the plane are 7.4cm and 6.1cm.

Given:
AB – segment;
AA1 = 7.4 cm;
BB1 = 6.1 cm;
C – middle AB;
CC1 =?
Decision:
The figure bounded by segments AB, AA1 and BB1 (distance from points A and B to the plane) and A1B1 (segment on the plane) is a trapezoid (ABB1A1). The distance from the middle of the line segment AB to the plane (CC1) will be the middle line of the trapezoid.
The middle line of the trapezoid is equal to half the sum of the bases. Then in the trapezoid ABB1A1 the middle line CC1 is equal to:
CC1 = (AA1 + BB1) / 2;
CC1 = (7.4 + 6.1) / 2 = 13.5 / 2 = 6.75 (see);
Answer: 6.75 cm.



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