The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.
A = (0,0), B = (3,4), C = (4,-3)

A)
B)
C)
D)

Question

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0), B = (3,4), C = (4,-3)
​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

Using the distance formula, we can calculate that AB has length 5, BC has length $\sqrt{41}$, and AC has length 5. Therefore, this is a triangle with sides of lengths 5, $\sqrt{41}$, and 5. Using the Pythagorean Theorem, we can verify that the angle opposite side BC is acute, and therefore the triangle is not a right triangle. The point C has a negative y-coordinate, which means it lies below the x-axis, so the triangle is not isosceles. Therefore, the only remaining option is scalene, which is satisfied by the triangle with vertices A = (0,0), B = (3,4), and C = (4,-3).

The Given Points Represent the Vertices of a Triangle