Question

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

Answer 1

C.

y4 - y3/x4 - x3

X

y2 - y1/ x2 - x1 = -1

Explanation:

Took it on edmentum/plato its right. enjoy :)

Answer 2

Calculate the lengths of the sides of the triangle:

`\overline{DE}=√((8-7)^2+(1-3)^2)=√(1^2+(-2)^2)=√(1+4)=√(5) \\ \overline{DF}=√((4-7)^2+(-1-3)^2)=√((-3)^2+(-4)^2)=√(9+16)=√(25)=5 \\ \overline{EF}=√((4-8)^2+(-1-1)^2)=√((-4)^2+(-2)^2)=√(16+4)= \\ =√(4(4+1))=√(4 * 5)=2√(5)`
The triangle has three different sides, so it's a scalene triangle.

Now if c is the longest side of the triangle, and a and b are the shorter sides, then:
- if
`c^2=a^2+b^2`, the triangle is right
- if
`c^2<a^2+b^2`, the triangle is acute
- if
`c^2>a^2+b^2`, the triangle is obtuse

The longest side is 5.

`c^2=5^2=25 \\ a^2+b^2=(√(5))^2+(2√(5))^2=5+4 * 5=5+20=25 \\ \Downarrow \\ c^2=a^2+b^2`
The square of the longest side is equal to the sum of the squares of the shorter sides, so it's a right triangle.

The triangle is a right scalene triangle.