What type of triangle has vertices at (-a,0), (a,0), and (0,b)?
A) right
B) obtuse
C) equilateral
D) isosceles

Question

Quizplus · Accepted Answer

The triangle has two sides of equal length (distance between (-a,0) and (a,0)), so it is either isosceles or equilateral. To determine which, we need to consider the third side. The distance between (-a,0) and (0,b) is $\sqrt{a^2+b^2}$, and the distance between (a,0) and (0,b) is also $\sqrt{a^2+b^2}$. So all three sides have the same length, making it an equilateral triangle. However, if we didn't recognize that the third side was the same length as the other two, we might have guessed that it was isosceles.

What Type of Triangle Has Vertices at (-A,0), (A,0), and (0,b)