What type of triangle is formed by joining the points d(7,3) e(8,1) and f(4,-1)?

A right triangle  

Step-by-step explanation:

If you plot the triangle as in the figure below, it looks like a right triangle.

It should satisfy Pythagoras' Theorem:

   AB²    +     AC²   =    BC²

Each side of the triangle is the hypotenuse of a smaller right triangle.

(2² + 4²) + (2² + 1²) = (4² + 3²)

(4 + 16)  +   (4 + 1)   =  16 + 9

   20     +       5      =      25

            25             =      25

The theorem is satisfied. ∆ABC is a right triangle.

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step-by-step explanation: