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To have a better visualization, you have to graph the points by hand or by using a software like MS Excel. By graphing, you will see that the triangle being formed is a right triangle. This is because a right angle is being formed by angle DEF. Hope this answers the question.
isyllus

Answer:

DEF is a right angle triangle.

Step-by-step explanation:

Given: Three coordinate of triangle.  D(7, 3), E(8, 1), and  F(4, -1)

Using distance formula to find the length of side of triangle.

[tex]DE=\sqrt{(8-7)^2+(1-3)^2}=\sqrt{5}[/tex]

[tex]EF=\sqrt{(8-4)^2+(1+1)^2}=2\sqrt{5}[/tex]

[tex]DF=\sqrt{(4-7)^2+(1+3)^2}=5[/tex]

DE≠DF≠EF

Thus, DEF is neither equilateral nor isosceles.

Using pythagoreous theorem,

[tex]DF^2=DE^2+EF^2[/tex]

[tex]5^2=(\sqrt{5})^2+(2\sqrt{5})^2[/tex]

[tex]25=25[/tex]

LHS  = RHS

So, Triangle DEF is satisfy the pythagoreous theorem.

Thus, DEF is a right angle triangle.

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