This is the hardest math problem I have ever been given. I'm not in honors math classes, and I'm a junior. I found this in the first chapter of a calculus textbook and I've been thinking about it for days.
>>9076911
this isn't even a calculus problem, this is basic middle school algebra
Man are you serious? Hardest problem you've ever seen? Lmao
>>9077344
I'm aware, it's in the first chapters. Introduction sort of deal.
>>9077355
Yeah, help me out here.
>>9078137
Underaged b&
>>9076911
this is the way to go:
https://en.wikipedia.org/wiki/Homothetic_transformation
>>9076911
Basically everything you need to understand what's going on is here
https://en.wikipedia.org/wiki/Triangle_center
>>9076911
The third one is completely obvious. The bottom of the triangle is parallel to the x axis, so the altitude for the point (b,c) is parallel to the y axis. It passes through (b,c), so the x coordinate for the intersection of the three points is b. Next, you take the slope of the line connecting (b,c) and (a,0) (c/(b - a)), and find the slope of the line perpendicular to it ((a-b)/c). Using the point slope formula with this slope and the point (-a,0) (because the second altitude contains (-a,0)), you can get an equation for the line representing the second altitude. Finally, set x = b in this equation so that you can find the y coordinate of the intersection of the two altitudes. Geometrically, all three are guaranteed to intersect the same point, so you don't need an equation for the third one. Perpendicular bisectors is obvious, the x coordinate is 0, and the y coordinate can be found by using the point-slope formula with aforementioned slope, but with the point ((a+b)/2, c/2) instead of (-a,0) (of course, you substitute x = 0 into the equation to find the y coordinate). Medians is easy, just use the linear equation formula where you plug in 2 different points (the first linear equation you need is the one made with (0,0) and (b,c), and the second is (-a,0) and ((a+b)/2,c/2)). Use elimination or substitution to solve the system of 2 equations.
off the top of my mind you could easily set up linear equations of most of these lines and set them equal to each other to solve for the unknowns. This is basic algebra/geometry and this is b8.
OP is pic related