# Core 1 - Show that its a right angle

Okk ive been doing some past papers, and in some of them they require you to show that 3 points given is a right angle or something like that and im not too sure on how to do this, could someone explain with the following question.

The triangle ABC, has vertices A(1,3), B(3,7) and C(-1,9)
a) i) find the gradient of AB and i got 2

ii). Show that angle ABC is a right angle, (dunno how to do this one)
Do you know how to find whether two lines are perpendicular?
Find the gradients of AB and BC and show that the lines are perpendicular, hence you have a right angle
If one line is at right angles to another, it is tangential, and the gradient of a tangent it -1/grad of original line.

Gradient of AB is 2 as you've found, so prove the gradient of BC is -1/2
Ahh right i get it now, the gradient of bc was -1/2 and x that by 2 = -1
Original post by Snammus
it is tangential

perpendicular*
Or you could work out the lengths of the three lines and show that they satisfy pythagoras theorem in the appropriate way.
But the gradient way is much quicker !
(edited 12 years ago)
Original post by Forum User
Or you could work out the lengths of the three lines and show that they satisfy pythagoras theorem in the appropriate way.
But the gradient way is much quicker !

I know this a really old thread, but it is possible for you to explain the first way since I did the Pythagoras Theroem way and I wanted to ensure I did it in the right way?
Original post by AnotherAnomaly
I know this a really old thread, but it is possible for you to explain the first way since I did the Pythagoras Theroem way and I wanted to ensure I did it in the right way?

Using Pythagoras, you can work out each length. For example, for length AB, you can construct a right-angled triangle with AB as the hypotenuse. You can work out the two other lengths by using the coordinates to work out the change in x as the horizontal length and the change in y as the vertical one. Once you've done that, you should see that the two lengths you have are 2 and 4. Plug these into Pythagoras' Theorem and you get 2√5 (or √20) as the length for AB. After having done the same for both BC and CA, you should see that √(AB²+BC²) = CA². I hope that helps.
Original post by AnotherAnomaly
I know this a really old thread, but it is possible for you to explain the first way since I did the Pythagoras Theroem way and I wanted to ensure I did it in the right way?

ai) gets you to show the gradient of AB is 2.
If the gradient of BC = -1/2 then theyre perpendicular as they multiply to give -1 and you have a right angled triangle.

Its probably a bit simpler to do this and follows from the first question part, but pythagoras is easy enough.