Prove that the points (2,-2), (-2,1) and (5,2) are the vertices of a right-angled triangle. Also, find the area of the triangle.

SARAHann
Apr 1, 2017

#1**+1 **

Find the lengths of the triangle's edges and use the pythagoras theorem. Good luck.

Ehrlich
Apr 1, 2017

#2

#3**0 **

yes. i got the answer. but when i first attempted the question i changed the co-ordinates of the vertices. if the co-ordinates are changed we don't get a right answer right? The first one is mine and the 2ed one is alan's.

SARAHann
Apr 1, 2017

#5**+1 **

no, we WILL get a right triangle. You simply wrote 'B' instead of 'A', 'C' instead of 'B' and 'A' instead of C. it doesnt change the fact its a right triangle. well yes, in alans picture the angle b=90. in your inaccurate picture (which is probably the reason you got confused) c=90.

its like calling x 'n' in x*2+3=5 and thinking the answer will be different. it wont. you didnt change anything besides the letters and it doesnt matter. dont worry, you got the right answer.

Ehrlich
Apr 1, 2017

#7**0 **

But in my dig angle b=90. my co-ordinated were in the wrong places so my answer was wrong.

my working was like this: (as per the 1st dig)

AB=\(\sqrt{}25 = 5\)

BC =\(\sqrt{}50 =5\sqrt{}2\)

AC= \(\sqrt{}25 = 5\)

using pythagoram theorm, AC²=AB²+BC²

5=5²+\(5\sqrt{}2\)²

5 not = 25+50

But as per Alan's dig:

AB=\(\sqrt{}25 = 5\)

BC =\(\sqrt{}25 = 5\)

AC=\(\sqrt{}50 =5\sqrt{}2\)

using pythagoram theorm, AC²=AB²+BC²

\(5\sqrt{}2\)²=5²+5²

50=25+25=50

SARAHann
Apr 1, 2017

#9**+2 **

Ok i think i know how to explain it to you.

when you first learned the pythagoras theorem, the teacher probably drew a right triangle on the board. The teacher then marked the right angle with the letter 'B' and said that (AB)^{2}+(BC)^{2}=(AC)^{2}.

The teacher was right. But you forgot something. You dont have to mark the right angle with 'B'. The teacher coulve marked it with 'C'. That means instead of (AB)^{2}+(BC)^{2}=(AC)^{2 }the theorem would've been (BC)^{2}+(AC)^{2}=(AB)^{2}. You dont need to mark something with a specific letter for it to work.

what you did wrong is you marked a specific angle with B and thought it means B is the right angle! but thats wrong, because 'A' is the right angle!.

also, in my first post i wrote:

You simply wrote 'B' instead of 'A', 'C' instead of 'B' and 'A' instead of 'C'.

I was wrong, i dont know if it helps you but you wrote 'A' instead of 'B', 'B' instead of 'C' and 'C' instead of 'A'.

hope it helps!

Ehrlich
Apr 1, 2017

#10**0 **

yes i know that. the letters can be changed but i did'nt understand by what u meant as

"what you did wrong is you marked a specific angle with B and thought it means B is the right angle! but thats wrong, because 'A' is the right angle!."

but B is the right angle ryt?

SARAHann
Apr 1, 2017