Intersection between unknown functions

I have different plots that have no function. One type of plot is from a csv.file that I got 34 plots and the other 2 are lines of 2 points. So I want to find the intersection between each line of plot(x,y) inside the loop and those 2 other lines (see the picture).

clc 
clear
data = readtable('Group 4 (Trajectories).csv');
Trajectory_index = data(:,1);
MMSI = data(:,2);
Longitude = data(:,4);
Latitude = data(:,5);

figure(); hold on

for i = 1:1:34
    idx = data.Trajectory_index == i;
    newTable = data(idx,:);
    x = newTable.Latitude;
    y = newTable.Longitude; 
    axis([36.4 42 -10.5 -9]);
    plot(x,y);
end 

x1 = ([38.7091 38.715]);
y1 = ([-10.1466 -10.0655]);
plot(x1, y1);

x2 = ([37.8602 37.8927]);
y2 = ([-10.0353 -9.8046]);
plot(x2, y2);


hold off 
shg 

Answer 1

[Walter Roberson]

    x = newTable.Latitude;
    y = newTable.Longitude; 

At that point, use https://www.mathworks.com/matlabcentral/fileexchange/93470-intersections-of-multiple-2d-lines-or-line-segments

Originally I was going to suggest using interp1() but then I noticed the line segments are slightly sloped.