How to make an animation of changing dimension rectangle in Matlab?

I am trying to do an animation, with a rectangle, which should change dimension every time it touch the wall (taller and thinner). I did something like that, and it is not so bad, but area should be always the same and now it is not. Other bad thing is that it is not touching right wall. And it should be always on this same height but it's not. Can You please help me with these problems?

My code:

clear all;
clc;

x=[0 0 100 100 0];
y=[0 100 100 0 0];

plot(x,y,'black');
axis([-10 110 -10 110]);
hold on;
g = hgtransform;
x=[50 50 100 100 50];
y=[37.5 62.5 62.5 37.5 37.5];
patch('XData',x,'YData',y,'FaceColor','white','Parent',g)
pt1 = [-50 0 0];
pt2 =[1 1 1]
for i=1:1:1000

for t=linspace(0,1,250)
  b = makehgtform('scale',pt2,'translate',t*(pt1));
  set(g,'Matrix',b)
  drawnow
end

pt2=pt2+[-0.125 0.125 0];

for t=linspace(1,0,250)
  b = makehgtform('scale',pt2,'translate',t*(pt1));
  set(g,'Matrix',b)
  drawnow
end
pt2=pt2+[-0.125 0.125 0];
end

Answer 1

[Ameer Hamza]

clc;
x=[-50 -50 50 50 -50];
y=[-50 50 50 -50 -50];
plot(x,y,'black');
axis([-60 60 -60 60]);
hold on;
x=[-25 -25 25 25 -25];
y=[-12.5 12.5 12.5 -12.5 -12.5];
p = patch('XData',x,'YData',y,'FaceColor','white');
pt2 = [1 1 1];

time_instants = 250;
for i=1:1:1000
    % right to left
    right_max = 50 - max(x);
    left_max = -50 - min(x);
    for t=linspace(right_max, left_max, time_instants)
        p.Vertices(:,1) = x' + t;
        drawnow
    end
    pt2=pt2+[-0.125 0.125 0];
    x = x*pt2(1);
    y = y*pt2(2);
    p.Vertices(:,2) = y;
    
    % left to right
    right_max = 50 - max(x);
    left_max = -50 - min(x);
    for t=linspace(left_max, right_max, time_instants)
        p.Vertices(:,1) = x' + t;
        drawnow
    end
    pt2=pt2+[-0.125 0.125 0];
    x = x*pt2(1);
    y = y*pt2(2);
    p.Vertices(:,2) = y;
end