Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4, -1)?

Answer 1

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Answer 2

$D(7,3) \\ E(8,1) \\ F(4,-1)$

The lengths of the sides of the triangle:
$\overline{DE}=\sqrt{(8-7)^2+(1-3)^2}=\sqrt{1^2+(-2)^2}=\sqrt{1+4}=\sqrt{5} \\ \\ \overline{DF}=\sqrt{(4-7)^2+(-1-3)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5 \\ \\ \overline{EF}=\sqrt{(4-8)^2+(-1-1)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}= \\ =\sqrt{4 \times 5}=2\sqrt{5}$

No sides are equal to each other, so it's a scalene triangle.

Check if the sides satisfy the Pythagorean theorem:
$(\sqrt{5})^2 + (2\sqrt{5})^2=5^2 \\ 5+20=25 \\ 25=25 \\ true$
They do, so it's a right triangle.

The triangle is a right scalene triangle.