I agree, Lucas, and I'm excited about that. Not that I get excited that people don't understand, but I do get excited about having people willing to struggle, and to put in effort to find resources to gain understanding.
Thanks so much!! You're like that one rare math youtuber who actually teaches math well and makes it straight to the point. Thank you so much for helping
holy crap dude. I've searched for over an hour for a good explanation for this because I've forgotten it from math class. you've just made my math project so much easier! Thanks!
Oh my gosh, I can't thank you enough for this video. I was literally getting so upset because I couldn't figure out altitudes and when I saw your video it immediately made sense to me. Thank you so much, you are a life saver 😀😄👍🏻
Ashlea Camarra, I couldn't reply back directly to your question, so I hope you see this. I don't have the time to create a video at the moment, but I want to at least give you something to go on. For that triangle, you're going to be doing the same thing as in the video. If it helps, put the points on a graph, and notice you have to go down and right along the line AC to get to R, where CR would be perpendicular to AC. Then do what we did before: Find the slope of AC, then get its opposite reciprocal, which is the slope of AC. Use that slope, and B, to get the equation of the line BR. If that doesn't make sense, email me at school at dann(at)daytonsd.org and I'll try to be more clear.
Thank you for explaining this! I understand it so much better now! Would you be able to explain how you would find the equation of an altitude that was outside the triangle? I have an assignment where I need to find the equation of the altitude but it is outside an obtuse triangle. The points are A(-2,10), B(2,-4) and C(4,6) and I have to find the altitude equation of altitude BR. Could you please help me understand how to do this? Thank you so much!
Yihao, I'm happy to help you, but I need more information. If all you were given about side AB was the coordinates of A and B, or maybe just it's length, then you can't answer. Is there any other information given?
I'm glad the videos were helpful. I know they're old, and they're not very fancy, but I find that some people just want to have things explained to them simply. Best to you.
If you were in my class, I'd smile reassuringly and say, "No, but I see what you mean, so yes." Flipping it over doesn't make it negative it just finds the reciprocal. But you want the opposite reciprocal, so yes, after you flip it over, make it negative. Clarifying (hopefully): perpendicular lines have slopes that are opposite reciprocals. One is positive, the other is negative and 'flipped over.'
bit late, but this is the only video that explained it to me well. Its been 13 years since this was posted and I couldn't find a better explanation. Definitely better than my teacher and tutor.
The problem I'm doing is on an obtuse isosceles triangle. It doesn't give me the points, only the length of one side (the base) which is 10. How do I solve that problem?
Eva, If they only gave you the length of one side, then you can't get the equation. There needs to be some information about the location of one of the points, or perhaps some angles. If you'd like, you can snap a picture of the problem and sent it to me at dann (at) daytonsd (dot) org. I'll be happy to help.
I'm so sorry I didn't see this earlier. I hope you got your question answered in some way. I would find the midpoint of BC if I was finding the equation for a 'median,' which goes from a vertex to the midpoint of the opposite side. Since I'm find an 'altitude,' which intersects the opposite side at a right angle, then the midpoint isn't relevant. Best to you.
Ryan, if you're asked to find the equation of an altitude CP in a triangle with vertices A, B and C, then you'd be looking for the equation of a line through C to a point on AB. That line has to hit AB at a 90 degree angle. So it will likely not be the midpoint at all. (That would only happen if triangle ABC is isosceles with AC and AB being congruent.) If you're finding an altitude, then use the technique I showed in this video. If you truly need to find a line from C to the midpoint on AB, then I have a video that shows that as well. (Find the Equation of a Median in Triangle) Hope that helps.
Hi sir :)... I'm just curious to ask something... How if for example, the slope of line BC = 0? Is the slope of the altitude undefined? Do I still need to find the altitude's equation if that happens? And what is the intersection point of the altitude's equations?
+Maria Angela San Pedro Great questions, Maria! I'll address them one at a time. 1) Yes, if the slope of BC is zero (ie it's horizontal), the the altitude through it is vertical, so it does have undefined slope. It's equation, if you need to find it, will be in the form x = #, where # is the x-coordinate of A. 2) If you need to find the intersection of the altitudes (the orthocenter), first, find the equations for two of the altitudes. (All three meet at a single point, but you only need two.) The video shows that the one through A is y = 1/4x + 2. The one through B is y = 3x - 12, which I found using the same method shown. Now you need to find the coordinates of the point where these two lines meet. To me, the easiest way is to recognize that since their left sides are equal to each other, then so are their right sides. So write this as an equation and solve: 1/4x + 2 = 3x - 12 14 = 11/4x (add 12 and subtract 1/4x from each side) 56/11 = x (divide by 11/4) Now substitute this value for x into either of the equations to find the y-coordinate. I'll use the first. y = 1/4(56/11) + 2 = 36/11. So the intersection is at (56/11 , 36/11).
I would have gotten the same result either way. I just need to have the difference in y coordinates divided by the difference in x-coordinates. So I had no preference.
Kevin, I'm going to make the assumption that you either know how to find the hypotenuse (long side) of a right triangle, or that you're going to go watch a video on it. If you have that skill (finding the long side of a right triangle given the two short sides), then you're ready to go with finding the distance between the vertex and the point you found on the opposite side. For this part, you could look up a video for 'finding the distance between two points' or the 'Pythagorean Distance Formula.' Here's the basic idea: Draw a vertical line through one of the points, and a horizontal line through the other. You'll notice that these two lines, plus the altitude, make a right triangle. You can get the length of the horizontal side by subtracting the x-coordinates of two points. You can get the length of the vertical side by subtracting the y-coordinates. Now you have the lengths of the two short sides of the triangle, and you can find the length of the long side (the altitude) using the Pythagorean Theorem. Hope that helps.
I'm really sorry. I don't understand your question. Happy to help if I can. If it helps, rewatch the video and tell me the time in the video for the part that doesn't make sense and I'll try to help from there.
If I subtract y1-y2, and you subtract y2-y1, we'll get numbers that the are the opposite of each other. Same with x1-x2 and x2-x1. If we each do a division, but your numbers are both the opposite of mine, shouldn't we get the same answer?
Hi Jennifer. I'm assuming that you're talking about a triangle where the obtuse angle is NOT the one with the altitude going through it. But it will work the same way. Find the slope of the line through the two points that form the opposite side of the triangle, then find its opposite reciprocal. That will be the slope of the line you're looking for. Then you'll finish out the problem the same way. Good luck.
Excellent question. You would find the midpoint if you were finding a median, since a median goes through a vertex and the midpoint of the opposite side. But altitudes go through the vertex and are perpendicular to the opposite side. So no need for midpoints. You'll need a point and slope to get the equation. You've got the vertex for the point, but you'll have to get the slope by finding the slope of the opposite side, the finding its opposite reciprocal to get the slope of the altitude (since they are perpendicular). Then you're ready to find the equation. (Side note: If the triangle happened to be isosceles, and you were finding the altitude through the vertex connecting the two congruent sides, then you could find the midpoint and make it work, since the altitude and median would be the same line. Be careful though, your teacher might want you to prove that claim before you use it.) Good luck.
That is right if you intended for B to be the initial and C to be the second. But he switched them around, and I did the maths, its still right! 6--2/6-8=-4 and -2-6/8-6=-4. Good spot.
Thanks, Edward, for helping Mandeep out. That's the way math class ought to run! You're exactly right. It doesn't matter which way you decide to subtract, AS LONG AS you subtract the same direction on both of them. Mandeep, keep asking good questions, even if you end up feeling a little silly afterward. I'd rather have students (or employees) that ask questions to be sure they understand, rather than those who just keep quietly out of fear of looking wrong.
