Find the equation of the line of symmetry of the trapezoid whose vertices are A(0,0), B(10,0), C(6,4), D(4,4).

Step-by-step solution

1. Check if the trapezoid is isosceles: compute AD and BC lengths. AD = √((4-0)²+(4-0)²) = 4√2. BC = √((6-10)²+(4-0)²) = 4√2. Since AD = BC, it is isosceles.
2. The axis of symmetry of an isosceles trapezoid is the perpendicular bisector of its bases.
3. Find midpoints of bases AB and CD. Midpoint of AB: ((0+10)/2, (0+0)/2) = (5,0). Midpoint of CD: ((6+4)/2, (4+4)/2) = (5,4).
4. The line through these two points is vertical: x = 5.
5. Thus the equation of the line of symmetry is $x=5$.

Concept tested: Symmetry of isosceles trapezoid

Published 10 October 2026 · How this solution was prepared and checked