import geometry;

pen emergenceStyle = dotted;
pen transformationStyle = lightred;
pen axisStyle = longdashdotted + heavyred;
pen topStyle = blue;
pen botStyle = green;

size(5cm);

point A = (-3, 0);
point D = (-2, 4);

line axis = Oy;

transform reflect = reflect(axis);

point B = reflect * A;
point C = reflect * D;

draw(axis, axisStyle);

path trapezoid = A--B--C--D--cycle;
draw(trapezoid, emergenceStyle);

dot("$A$", A, SW, botStyle);
dot("$A^\prime$ = B", B, SE, botStyle);
dot("$D^\prime$ = C", C, NE, topStyle);
dot("$D$", D, NW, topStyle);

real little = 0.3;

real dTop = distance(A, axis);
real dBot = distance(D, axis);

point PTop = midpoint(A--B) + little*dTop*N;
point PBot = midpoint(C--D) + little*dBot*N;

path reflTop = A..PTop..B;
path reflBot = C..PBot..D;

draw(reflTop, transformationStyle, Arrows, Margins);
draw(reflBot, transformationStyle, Arrows, Margins);