Triangle ABC have vertices #A(0,4)#, #B(1,2)#, and #C(4,6)#. Is triangle ABC a right triangle?
We can solve this by using vectors. Let's start by defining
To figure out whether two lines are perpendicular or not (that means that they cause a 90 degree angle between them), we can multiply the two vectors together. If the product is 0, it means that they indeed are perpendicular.
Let's see if whether:
When we are multiplying vectors (dot multiplying), we multiply the x components together, and add them with the product of the y components.
Let's start with
Well, that was lucky! Now we know that AB is perpendicular with AC, because
Hope this helped. If you don't know how to use vectors, I'm sorry to say that I don't know another way of proving this.