Determine the name of the following triangle using the given points:
A(5,6), B(-1,-2) and C(-3,2). Be as specific as possible.
I used the distance formula and found that AB had a side of 10
BC had a side of 2 sqrt 5
CA had a side of 4 Sqrt 5
I found that since all sides are different, it is a scalene triangle.
Can you please tell me if I am correct?
ahhh, but did you also notice that
(2√5)^2 + (4√5)^2 = 10^2
So what else do you know about the triangle ?
Ok, so you're using the pathagorean theorum. I'm a bit rusty on my geometry so does that make it a right scalene?
yup!
:) Thanks!
Yes, you are correct in determining that the triangle is a scalene triangle.
To further determine the name of the triangle, we can also examine the angles. Since we know the coordinates of each point (A, B, and C), we can use the distance formula to find the lengths of AB, BC, and CA. Based on the lengths you have provided (AB = 10, BC = 2√5, CA = 4√5), we can see that all three sides have different lengths, which is a characteristic of a scalene triangle.
Therefore, we can confidently conclude that the name of the triangle with points A(5,6), B(-1,-2), and C(-3,2) is a scalene triangle.