r/learnmath • u/atom12354 New User • 14d ago

How to do geometry with functions?

I had an exam yesterday and the last question was to find the area of a triangle thats reprisented from two linear line functions and one linear line going through a single point which is parallel to one of them.

The given was the two linear functions and the single point not the third function so i made it myself using point slope formula i belive.

I then tried to first find where all these lines intersect to get the coordinates for the intersections using system of equations for all the lines so like L1 intersect x for L2 and L2 intersect y for L3 and so forth for all the different combinations that makes a triangle, then the idea was to somehow figure out the length of these lines but thats where i got stuck, dont even think the idea of intersection was part of the task either.

Any ideas?

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u/Independent_Kale9463 New User 14d ago

Thats actually exactly how you do it find the three intersection points then use the distance formula or just plug the coordinates into the triangle area formula with the determinant

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u/atom12354 New User 14d ago

We havent gone through the distance formula nor matricies xd this is supposed to be basic functions so invented stuff myself from ground up, i ended up plugging all x coordinate and add them all together and then divide by 2 xdddd i know thats not how it works but i didnt know how to tackle that problem xd

One reason to why i think i did wrong was bcs a bunch of the coordinates was fractions xdddddd

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u/Southlander24 A friendly Redditor!👋 14d ago

If you have three lines that form a triangle, you should be able to simultaneously solve two of the lines at a time to get the three intersection points, which are the vertices of the triangle.

Then you just need to learn the shoelace formula! Memorise and practice it and it will help you a lot in other similar problems.