Solving geometry problems Solve it
values in the problem statement. Isn’t that cool?
How about finding the intersection point of two straight lines? Let us have the following two straight lines, defined in the Cartesian coordinate system, i.e., the x-y system: 4x + 3y = 24 3x + 4y = 25
Similar to the earlier problem, the intersection point could be obtained as follows: $ octave -qf octave:1> A = [ >43 >34 > ]; octave:2> b = [ > 24 > 25 > ]; octave:3> u = inv(A) * b u= 3.0000 4.0000
octave:4>
So, (3, 4) is the intersection point. If you want to see it visually, you just need to rewrite the straight line equations as follows: y = (24 – 4x) / 3 y = (25 – 3x) / 4 And then here is the code: octave:1> x=-10:0.01:10; octave:2> plot(x, (24 - 4*x)/3, “b.”, x, (25 - 3*x)/4, “g.”); octave:3>
Figure N shows the graph generated by the above code. Equipped with the basics of puzzle solving, here’s one to tease your brain with: A vegetable seller has placed various equally priced stacks for sale at ` 3M. One stack has 4 lemons, 7 cucumbers and 9 tomatoes. Another has 2 lemons, 5 cucumbers and 27 tomatoes. And the third has just 9 cucumbers and N5 tomatoes. Can you compute the price of each vegetable?
Hint: Assume the price of lemons, cucumber, and tomato as ‘l’, ‘c’, and‘t’, and then form the three equations in three variables.
If you think, you have got it, you may email the solution to me. And as we move on, we will get into some different kind of puzzle-solving.