1 Attachment(s)

Triangle problem in coordinate geometry

I have a triangle with two vertices known (1,3) and (-4,1).

I know a formula relating the acute angle formed by two lines and their slopes. It is

I used this formula for the hypotenuse and one of the sides(m1) and then again used this formula for the hypotenuse and the other side(m2). I used the result m1m2=-1 in the second result and got two values of m1. But when I equate those values I get tanA=0.

What is wrong?

Re: Triangle problem in coordinate geometry

What do you want to find out, for drawing a triangle we need to know three elements?

Re: Triangle problem in coordinate geometry

I don't want to find anything. I am just not able to understand why I am getting tanA=0 when it could be anything.

Re: Triangle problem in coordinate geometry

Please show your work that will make this clear. In fact where are the slopes of tow other sides of the triangle? I Sri think some information is missing. With only this much information we gat infinitely many triangles and hence the problem?

Re: Triangle problem in coordinate geometry

there is no other information. I don't know what I am doing wrong with the information that is provided.

slope of hypotenuse=2/5

putting this in the formula for tan A.We get

Similarly, I found m2 in terms of tan A and replaced m2 with -1/m1 to get

On equating these two values of tanA I get tanA=0.

Re: Triangle problem in coordinate geometry

appears to be the slope of a vertical line. But, if it is not, then you can calculate it using . (note: this slope is not defined if ).

Then appears to be the slope of a horizontal line. Still, we can calculate it: (note: this slope is not defined if ).

Then, you would have

Simplifying, you get

Is that what you were looking for?

Re: Triangle problem in coordinate geometry

I was not looking for anything. I am just getting a wrong result that is **tanA=0** but I am not able to find mistake in my work.

Re: Triangle problem in coordinate geometry

Oh, I misread the problem. This may not be the solution. The calculation I gave was for the angle between the lines with slopes , not angle . Also, if you are suggesting that the two lines are perpendicular, then

So, possibly this would be helpful The second equation just came from finding the length of each segment.

Then, simplifying the LHS and squaring both sides, you have:

Apparently, this has solutions at over the integers, and over the reals, it has solutions or and .

Re: Triangle problem in coordinate geometry

How did you get the solutions. It has infinite solutions.

Re: Triangle problem in coordinate geometry

Re: Triangle problem in coordinate geometry

But all that was given was a line segment with an arbitrary point(x,y). It could have lied at any point on the circle with the line segment as the diameter.

Re: Triangle problem in coordinate geometry

That's a good point. I dunno. Weird that Wolframalpha gave solutions...

Re: Triangle problem in coordinate geometry

please tell me my mistake in post 5.

Re: Triangle problem in coordinate geometry

The line with slope is not adjacent to angle . Your formula requires the slopes of two lines that intersect at angle .

Re: Triangle problem in coordinate geometry