Question

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

F(4, -1)?
equilateral triangle
isosceles triangle
right triangle
acute scalene triangle
obtuse scalene triangle

Answer 1

Right triangle would be the answer your looking for>

Answer 2

Option C is the answer.

Explanation:

A triangle is given with vertices as D(7,3) E(8,1) and F(4,-1).

Now side DE =
`\sqrt{(7-8)^(2)+(3-1)^(2)`

=
`\sqrt{1^(2)+2^(2)}=√(1+4)=√(5)`

Side EF =
`\sqrt{(8-4)^(2) +(1+1)^(2) } = \sqrt{4^(2)+2^(2) }`

=
`√(16+4)= √(20)`

Side DF =
`\sqrt{(7-4)^(2)+(3+1)^(2) } = \sqrt{3^(2)+4^(2)}`

`=√(16+9) = √(25)`

Now for right angle triangle

DF²≡ EF² + DE²

`(√(5))^(2) + (√(20))^(2)= 5^(2)`

25 = 25

Therefore, the given triangle is a right angle triangle.

Option C is the answer.